scholarly journals Normal partitions of idempotents of regular semigroups

1978 ◽  
Vol 26 (1) ◽  
pp. 110-114 ◽  
Author(s):  
P. G. Trotter
Keyword(s):  
Regular Semigroup ◽  
Subject Classification ◽  
Regular Semigroups ◽  
M 10 ◽  
20 M 10

AbstractA characterization is provided here for any normal partition of the set of idempotents of a regular semigroup S. As a by-product of the method used, a new characterization of the greatest congruence on S corresponding to a given normal partition of its idempotents is obtained.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 M 10.

scholarly journals A characterization of the semigroup of matrix units

1980 ◽  
Vol 29 (3) ◽  
pp. 291-296
Author(s):  
Bernard R. Gelbaum ◽  
Stephen Schanuel
Keyword(s):  
Subject Classification ◽  
M 10 ◽  
20 M 10 ◽  
The Matrix ◽  
Matrix Units

AbstractLet I be a set and let (I) denote the set consisting of the 0 matrix over I × I and the matrix units over I × I. Then for x, z in (I) and x≠0≠z, xyz≠0 has precisely one solution y. This and several other statements are shown to be equivalent characterizations of (I) regarded as a semigroup with zero.1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

scholarly journals On the lattice of congruences on an eventually regular semigroup

1985 ◽  
Vol 38 (2) ◽  
pp. 281-286 ◽  
Author(s):  
P. M. Edwards
Keyword(s):  
Regular Semigroup ◽  
Subject Classification ◽  
Maximum Element ◽  
M 10 ◽  
Natural Equivalence ◽  
20 M 10 ◽  
Complete Sublattice ◽  
Eventually Regular Semigroup ◽  
Lattice Of Congruences

AbstractA natural equivalence θ on the lattice of congruences λ(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that θ is a congruence, each θ-class is a complete sublattice of λ(S) and the maximum element in each θ-class is determined. 1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

scholarly journals On when a topologically simple semigroup is simple

1978 ◽  
Vol 26 (1) ◽  
pp. 126-128
Author(s):  
Kermit Sigmon
Keyword(s):  
Open Problem ◽  
Simple Semigroup ◽  
Infinite Order ◽  
Compact Semigroup ◽  
Subject Classification ◽  
Locally Compact ◽  
M 10 ◽  
Compact Semigroups ◽  
20 M 10

AbstractThe compact semigroups in which each topologically simple subsemigroup is simple are characterized as those in which no subgroup sontains an element of infinite order. It is also shown that a locally compact toplogically simple subsemigroup of a compact semigroup must be simple. The note closes with an open problem.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 15; secondary 20 M 10.

scholarly journals Group congruences on eventually regular semigroups

1988 ◽  
Vol 45 (3) ◽  
pp. 320-325 ◽  
Author(s):  
S. Hanumantha Rao ◽  
P. Lakshmi
Keyword(s):  
Regular Semigroup ◽  
Group Congruence ◽  
Regular Semigroups ◽  
Eventually Regular Semigroup ◽  
Lattice Of Congruences

AbstractA characterization of group congruences on an eventually regular semigroup S is provided. It is shown that a group congruence is dually right modular in the lattice of congruences on S. Also for any group congruence ℸ and any congruence p on S, ℸ Vp and kernel ℸ Vp are described.

scholarly journals Free completely regular semigroups

1984 ◽  
Vol 25 (2) ◽  
pp. 241-254 ◽  
Author(s):  
P. G. Trotter
Keyword(s):  
Regular Semigroup ◽  
Structure Theory ◽  
Completely Regular Semigroup ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Additional Operation ◽  
Alternative Characterization ◽  
Completely Regular Semigroups

A completely regular semigroup is a semigroup that is a union of groups. The aim here is to provide an alternative characterization of the free completely regular semigroup Fcrx on a set X to that given by J. A. Gerhard in [3, 4].Although the structure theory for completely regular semigroups was initiated in 1941 [1] by A. H. Clifford it was not until 1968 that it was shown by D. B. McAlister [5] that Fcrx exists. More recently, in [7], M. Petrich demonstrated the existence of Fcrx by showing that completely regular semigroups form a variety of unary semigroups (that is, semigroups with the additional operation of inversion).

V-regular semigroups

1981 ◽  
Vol 88 (3-4) ◽  
pp. 275-291 ◽  
Author(s):  
K. S. S. Nambooripad ◽  
F. Pastijn
Keyword(s):  
Regular Semigroup ◽  
Transformation Semigroup ◽  
Inverse Semigroups ◽  
Full Transformation ◽  
Regular Semigroups ◽  
Von Neumann ◽  
Biordered Set ◽  
Von Neumann Regular ◽  
Strongly Regular

SynopsisA regular semigroup S is called V-regular if for any elements a, b ∈ S and any inverse (ab)′ of ab, there exists an inverse a′ of a and an inverse b′ of b such that (ab)′ = b′a′. A characterization of a V-regular semigroup is given in terms of its partial band of idempotents. The strongly V-regular semigroups form a subclass of the class of V-regular semigroups which may be characterized in terms of their biordered set of idempotents. It is shown that the class of strongly V-regular semigroups comprises the elementary rectangular bands of inverse semigroups (including the completely simple semigroups), a special class of orthodox semigroups (including the inverse semigroups), the strongly regular Baer semigroups (including the semigroups that are the multiplicative semigroup of a von Neumann regular ring), the full transformation semigroup on a set, and the semigroup of all partial transformations on a set.

scholarly journals The 𝒥-classes of an inverse semigroup

1979 ◽  
Vol 28 (4) ◽  
pp. 427-432 ◽  
Author(s):  
C. J. Ash
Keyword(s):  
Lower Bound ◽  
Inverse Semigroup ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Subject Classification ◽  
Partially Ordered ◽  
M 10 ◽  
20 M 10

AbstractIt is shown, using the author's construction for ‘labelled semilattices’, that every partially ordered set, in which every two elements have a common lower bound, is isomorphic to the partiallyordered set of 𝒥-classes of some completely semi-simple inverse semigroup.1980 Mathematics subject classification (Amer. Math. Soc): primary 20 M 10, secondary 04 A 05, 08 A 05.

Characterization of New Lead-Based Monophosphate Tungsten Bronzes, Pbx(PO2)4(WO3)2m(6≤m≤10)

1998 ◽  
Vol 139 (2) ◽  
pp. 362-372
Author(s):  
P Roussel ◽  
A.C Masset ◽  
B Domengès ◽  
A Maignan ◽  
D Groult ◽  
...  
Keyword(s):  
M 10

scholarly journals Regular semigroups, fundamental semigroups and groups

1980 ◽  
Vol 29 (4) ◽  
pp. 475-503 ◽  
Author(s):  
D. B. McAlister
Keyword(s):  
Regular Semigroup ◽  
Partial Order ◽  
Direct Product ◽  
Homomorphic Image ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Natural Partial Order ◽  
Regular Semigroups ◽  
Necessary And Sufficient ◽  
Fundamental Semigroups

AbstractIn this paper we obtain necessary and sufficient conditions on a regular semigroup in order that it should be an idempotent separating homomorphic image of a full subsemigroup of the direct product of a group and a fundamental or combinatorial regular semigroup. The main tool used is the concept of a prehomomrphism θ: S → T between regular semigroups. This is a mapping such that (ab) θ ≦ aθ bθ in the natural partial order on T.

scholarly journals FACTORIZATION THEOREMS FOR MORPHISMS OF ORDERED GROUPOIDS AND INVERSE SEMIGROUPS

2001 ◽  
Vol 44 (3) ◽  
pp. 549-569 ◽  
Author(s):  
Benjamin Steinberg
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Classical Theory ◽  
Derived Category ◽  
Inverse Semigroups ◽  
Subject Classification

AbstractAdapting the theory of the derived category to ordered groupoids, we prove that every ordered functor (and thus every inverse and regular semigroup homomorphism) factors as an enlargement followed by an ordered fibration. As an application, we obtain Lawson’s version of Ehresmann’s Maximum Enlargement Theorem, from which can be deduced the classical theory of idempotent-pure inverse semigroup homomorphisms and $E$-unitary inverse semigroups.AMS 2000 Mathematics subject classification: Primary 20M18; 20L05; 20M17

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