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# Congruence relations on abstract semigroups. by Donald Beaton McAlister Published .

Written in English

Edition Notes

Thesis (M. Sc.)--TheQueen"s University of Belfast, 1963.

## Book details

The Physical Object
Pagination1 v
ID Numbers
Open LibraryOL20335899M

CONGRUENCES ON REGULAR SEMIGROUPS FRANCIS PASTIJN AND MARIO PETRICH ABSTRACT. Let S be a regular semigroup and let p be a congruence rela-tion on S. The kernel of p, in notation kerp, is the union of the idempotent p-classes. The trace of p, in notation trp, is the restriction of p to the set of idempotents of S.

Abstract. In this expository paper, we use a naive approach to the structure of inverse semigroups to motivate the introduction of P-semigroups and E-unitary inverse semigroups.A proof of the so-called P-theorem, due to W.D.

Munn, is used to simplify some existing results on inverse subsemigroups of, and congruences on, E-unitary inverse semigroups. In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements.

Every congruence relation has a corresponding quotient structure, whose elements are the. For questions about congruence relations, equivalence relations on an algebraic structure that are compatible with the structure.

abstract-algebra semigroups congruence-relations. asked Jan 13 at kam. 7 7 bronze badges. votes. 0answers A theorem is given below (in which the book said that it is used in justifying how the.

Abstract. Yu, Wang, Wu and Ye call a semigroup S τ -congruence-free, where τ is an equivalence relation on S, if any congruence ρ on S is either disjoint from τ or contains τ.A congruence-free semigroup is then just an ω-congruence-free semigroup, where ω is the universal determined the completely regular semigroups that are τ -congruence-free with respect to each of Author: Peter R.

Jones. abstract-algebra semigroups monoid inverse-semigroups. asked Mar 17 at 1Spectre1. abstract-algebra semigroups congruence-relations. asked Jan 13 at kam. 7 7 bronze badges. votes.

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Regular and Inverse Semigroups; Subsemigroups, Ideals, Bi-Ideals, and Quasi-Ideals; Homomorphisms; Congruence Relations and Isomorphism Theorems; Green’s Relations; Free Semigroups; Approximations in a Semigroup; Ordered Semigroups; Chapter 2: Semihypergroups Abstract; History of Algebraic Hyperstructures.

To complete the proof, we make use of properties of congruences and Green's relations on eventually regular semigroups, proved by P.M. Edwards , that generalized earlier results of Hall on.

Two semigroups S and T are said to be isomorphic if there is a bijection f: S ↔ T with the property that, for any elements a, b in S, f(ab) = f(a)f(b). Isomorphic semigroups have the same structure.

A semigroup congruence ∼ is an equivalence relation that is compatible with the. Congruence is a special type of equivalence relation which plays a vital role in the study of quotient structures of different Congruence relations on abstract semigroups. book structures. The purpose of this paper is to study the quotient structure of (n, m)-semigroup by using the notion of congruence in (n, m)-semigroup.

Firstly, the concept of homomorphism on (n, m >)-semigroup is introduced. Abstract In his paper “On quasiseparative ‘semigroup- ’s’”, Krasilnikova, Yu. and Novikov, B. have stu-died congruences induced by certain relations on a “semigroup”. They further showed that if the “semigroup” is quasi separative then the induced congruence is a semilattice congruence.

In this. General properties of the graphs that correspond to these relations were studied by M.S. Putcha in ,and the structure of semigroups in which the minimal paths in the graph corresponding. Abstract. Exactly as in semigroups, Green's relations play an important role in the theory of ordered semigroups—especially for Congruence relations on abstract semigroups.

book of such semigroups. In this paper we deal with the ℐ-trivial ordered semigroups which are defined via the Green's relation ℐ, and with the nil and Δ-ordered semigroups. We show that there is an inclusion-preserving bijection between the set of all normal subsemigroups of a semigroup S and the set of all group congruences on S.

We describe also group congruences on E-inversive (E-)semigroups. In particular, we generalize the result of Meakin (J. Aust. Math. Soc. –, ) concerning the description of the least group congruence on an.

On Regular Congruences of Ordered Semigroups Bo za Tasi c Ryerson University, Toronto ON M5V 0B5, CANADA [email protected] Abstract.

An ordered semigroup is a structure S = hS;; iwith a binary operation that is associative and a partial ordering that is compatible with the binary operation. For a given congruence relation. Two semigroups S and T are said to be isomorphic if there is a bijection f: S ↔ T with the property that, for any elements a, b in S, f(ab) = f(a)f(b).

Isomorphic semigroups have the same structure. A semigroup congruence \sim is an equivalence relation that is compatible with the semigroup operation. A congruence C on a semigroup S is called non-trivial if C is distinct from universal and identity congruences on S, and a group congruence if the quotient semigroup S/C is a group.

Every inverse semigroup S admits a least (minimum) group congruence C mg: aC mgb if and only if there exists e ∈ E(S) such that ae = be (see [14, Lemma III]).

bound semigroups. Introduction and preliminaries The concept of a perfect semigroup was introduced by agnerV . Groups are very well-known examples of perfect semigroups. Another examples of such semigroups are congruence-free semigroups S with the property S = S2 (i.e., S is globally idempotent ; note that perfect semigroups have this.

Abstract The theory we present was first introduced to the mathematical world in a monograph of J. Smith, devoted to varieties with permuting congruences. It was extended to congruence modular varieties in a paper by J. Hagemann and C. Herrmann, and has since been elaborated into an impressive machinery for attacking diverse.

Romano i.e. relation m on semigroup S deﬁned by (a,b) ∈ m ⇐⇒ b ∈ L(a) ∧a ∈ L(b) ∧a ∈ R(b) ∧ b ∈ R(a),and relation c(m) in particular.

Here, we continue our research of band anticongruence on semigroups with apartness. Let us remaind that a algebraic structure A has the (anti- congruence) congruence extension property if for any algebraic substructure.

: Abstract Algebra: Introduction to Groups, Rings and Fields with Applications (Second Edition) () by REIS, CLIVE; RANKIN, STUART A and a great selection of similar New, Used and Collectible Books available now at great prices. used for semigroups as well as for ordered semigroups.

If S= (S;) is an ordered semigroup, then (S;) is also an ordered semigroup, called the dual of Sand denoted S. A congruence on an ordered semigroup Sis a stable quasi-order which is coarser than. In particular, the order relation is itself a congruence.

Abstract. Exactly as in semigroups, Green’s relations play an important role in the theory of ordered semigroups—especially for decompositions of such semigroups.

In this paper we deal with the -trivial ordered semigroups which are defined via the Green’s relation, and with the nil and Δ-ordered semigroups. on complete congruence relations of concept lattices. In , Grätzer, Lakser, and B. Wölk showed how the approaches of  and  also apply.

The results of this paper were announced by the first author on Jat an invited lecture at the International Conference on Universal Algebra, Lattices, and Semigroups, at the.

Rosenfeld is the father of fuzzy abstract algebra. Kuroki is re sponsible for much of fuzzy ideal theory of semigroups. Others who worked on fuzzy semigroup theory, such as Xie, are mentioned in the bibliogra phy. The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup.

Decompositions of the congruence lattice of a semigroup. Proceedings of the Edinburgh Mathematical Society, Vol. 23, Issue. 02, p. Congruences and Green's relations on eventually regular semigroups. Journal of the Australian Mathematical Society, Vol. 43, Issue. 01, p. Abstract. form at the back of the book.

These are also available as one exposure on a standard 35mm slide or as a 17" x 23" black and white photographic print for an additional charge. Photographs included in the original manuscript have been reproduced xerographically in this copy.

Higher quality 6" x 9" black and white photographic prints are. Bull. Amer. Math. Soc. Vol Number 3 (), The equivalence, for varieties of semigroups, of two properties concerning congruence relations.

Aspects of order and congruence relations on regular semigroups. By Gracinda Maria dos Santos Gomes. Get PDF (8 MB) Abstract. On a regular semigroup S natural order relations have been defined\ud by Nambooripad and by Lallement. A description of λ and J in the\ud semigroups T(X) and PT(X) is presented.\ud In Chapter II, it is proved that.

Mcfadden; Congruence Relations on Residuated Semigroups (II), Journal of the London Mathematical Society, Volume s, Issue 1, 1 JanuaryPages –1 We use cookies to enhance your experience on our continuing to use our website, you are agreeing to our use of cookies. REPRESENTATION THEORY OF FINITE SEMIGROUPS 5 A J-class (respectively, R-class, L -class) is called regular if it contains an idempotent.

If eis an idempotent, then H e is a group, called the maximal subgroup at e. It is the group of units of the local monoid eSeand so it. NONDUALIZABLE SEMIGROUPS DAVID HOBBY Abstract. A family of semigroups is produced, none of which can be dualized.

One of the fundamental problems in the theory of natural dualities is the dual- izability problem, that of deciding which ﬁnite algebras are dualizable, generating a quasi-variety which admits a natural duality.‘ The maximum idempotent separating congruence on eventually regular semigroups ’, Semigroup Forum 74 (), –  Luo, Y.

and Li, X. L., ‘ Orthodox congruences on an eventually regular semigroup ’, Semigroup Forum 74 (), – By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J*,~-simple semigroups.

The result generalizes Petrich’s result on completely regular semigroups with Green’s relation H a normal band congruence or a regular band. A SPECIAL CONGRUENCE LATTICE OF A REGULAR SEMIGROUP MARIO PETRICH Abstract. Let S be a regular semigroup and C its lattice of congruences.

We consider the sublattice Λ of C generated by σ-the least group, τ-the greatest idem-potent pure, µ-the greatest idempotent separating and β-the least band congruence on S.

In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological group, as well as every connected locally compact Hausdorff cancellative commutative.

Abstract Auinger, K., The congruence lattice of a strict regular semigroup, Journal of Pure and Applied Algebra 81 () semigroups and certain partial homomorphisms between these partial groupoids.

The con- and universal relations on a set X are denoted by F. Semigroups connected with equivalence and congruence relations Tamura, Takayuki and Dickinson, Robert, Proceedings of the Japan Academy, Semigroups whose lattice of congruences is Boolean.

Hamilton, Howard and Nordahl, Thomas, Pacific Journal of Mathematics, Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled.

Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in by the French mathematician Marty. detailed proof may be found in Volume 1, Chapter 1 of the book by Cliﬀord and Preston , which is a standard reference for basic classical results and notation in semigroup theory.

There is an obvious dual result involving right reversible semigroups and groups of left quotients. Thereafter, Xiao and Zhang proposed the notion of rough completely prime ideals in semigroups based on congruence classes induced by congruence relations in For the combination of Pawlak’s rough set theory, fuzzy set theory and semigroup theory, Wang and Zhan [ 13 ] introduced the concept of rough semigroups based on congruence.2 Congruence Relations and Congruence-Based Zero-Divisor Graphs12 A general reference for abstract algebra is T.

W. Hungerford’s book , and a general reference for commutative ring theory is I. Kaplansky’s book . Semigroups are of particular interest to. Abstract Algebra: An Introduction: Edition 3 - Ebook written by Thomas W.