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ON SEMIGROUPS WHOSE IDEMPOTENT-GENERATED SUBSEMIGROUP IS APERIODIC

2004
*
International journal of algebra and computation
*

Acknowledgments The first and fourth author gratefully acknowledge support of FCT through CMUP and the FCT and POCTI Project POCTI/32817/MAT/2000 which

doi:10.1142/s021819670400202x
fatcat:5hcettoqbnbibmrne6fp5fbidy
*is*funded in cooperation with the European Community ... For a pseudovariety V of*semigroups*, we denote by EV the pseudovariety consisting of all*semigroups**whose**idempotent*-*generated**subsemigroup*belongs to V. ...*One*way to*generalize*these notions to*semigroups**is*to consider all*semigroups**whose*simple group divisors belong to H. Equivalently,*one**is*considering all*semigroups**whose*subgroups belong to WH. ...##
###
On a problem of M. P. Schützenberger

1980
*
Proceedings of the Edinburgh Mathematical Society
*

If D e *& then, as pointed out by Schiitzenberger, the

doi:10.1017/s0013091500003795
fatcat:5wceykozozcmlgemwlr4zpcjta
*subsemigroup*IG(S),*generated*by the*idempotents*of S, has only trivial subgroups. ... A class of finite*semigroups**is*called a genus if it*is*closed under homomorphic images,*subsemigroups*and finite direct products. ... Let S e % then the*subsemigroup*IG(S) of S,*generated*by the*idempotents*of S,*is**aperiodic*. Proof. Since S e % S divides GxA for some finite group G and finite*aperiodic**semigroup*A. ...##
###
Inverse semigroups determined by their lattices of convex inverse subsemigroups II

2003
*
Algebra Universalis
*

For some slightly narrower classes it

doi:10.1007/s000120300004
fatcat:jxm3o4d2v5hznerk45qf5pgkbm
*is*known that every Co -isomorphism of necessity induces an isomorphism*on*the semilattice of*idempotents*, yielding to theorems*on*their Co -determinability. ... In Part I of this paper we showed that the study of Co -isomorphisms of inverse*semigroups*, that*is*, isomorphisms between the lattices of convex inverse*subsemigroups*of two such*semigroups*, can be reduced ... We shall derive sufficiency from a*general*theorem*on*simple LF -distributive inverse*semigroups*,*whose*definition*is*evident. ...##
###
Finite aperiodic semigroups with commuting idempotents and generalizations

2000
*
Israel Journal of Mathematics
*

*whose*

*idempotents*commute. ... That

*is*,

*is*the pseudovariety

*generated*by finite

*aperiodic*inverse

*semigroups*equal to the pseudovariety of

*aperiodic*

*semigroups*with commuting

*idempotents*? ...

##
###
ON LATTICE ISOMORPHISMS OF INVERSE SEMIGROUPS

2004
*
Glasgow Mathematical Journal
*

An L-isomorphism between inverse

doi:10.1017/s0017089503001666
fatcat:i3yc6j2q55ayzde45o6my2coli
*semigroups*S and T*is*an isomorphism between their lattices L(S) and L(T ) of inverse*subsemigroups*. ... The hypothesis*on*the restriction to*idempotents**is*satisfied in many applications. We go*on*to prove theorems similar to the above for the class of completely semisimple inverse*semigroups*. ... But the kernel*is**generated*by b and so*is*trivial, that*is*, a*is**aperiodic*. 3 ⇒ 1. Suppose e*is*below every*idempotent*of a .*On*the*one*hand, if E a*is*infinite then, by hypothesis, e < a. ...##
###
Covers for regular semigroups and an application to complexity

1995
*
Journal of Pure and Applied Algebra
*

It

doi:10.1016/0022-4049(94)00151-0
fatcat:7pczhyf4ara23m2n7pdg7qyara
*is*shown that any regular*semigroup**is*a homomorphic image of a regular*semigroup**whose*least full self-conjugate*subsemigroup**is*unitary; the homomorphism*is*injective*on*the*subsemigroup*. ... As an application, the group complexity of any finite E-solid regular*semigroup**is*shown to be the same as, or*one*more than that of its least full self-conjugate*subsemigroup*(the*subsemigroup**is*completely ... An E-solid regular*semigroup**is*a regular*semigroup**whose**idempotent**generated**subsemigroup**is*completely regular; by [19] an equivalent condition*is*that the self-conjugate core*is*completely regular ...##
###
NORMALLY ORDERED SEMIGROUPS

2008
*
Glasgow Mathematical Journal
*

NOS = EI m POI and NOS ∩ A = N m POI, where A, EI and N denote the pseudovarieties of all

doi:10.1017/s0017089508004230
fatcat:p6qk4kxidnectb4k6s57gzfvgm
*aperiodic**semigroups*, all*semigroups*with just*one**idempotent*and all nilpotent*semigroups*, respectively, and ... POI denotes the pseudovariety of*semigroups**generated*all*semigroups*of injective order-preserving partial transformations*on*a finite chain. ...*whose**idempotents**generate*a J-trivial*semigroup*. ...##
###
Page 40 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

to E; the greatest

*idempotent*separating congruence*on*T¢*is*the equality relation; and for any inverse*semigroup*S*whose*subsemilattice of*idempotents**is*E there*is*an*idempotent*separating homomor- ... Then C,F,,,*is*the subvariety of F, consisting of the epigroups of Ff,*whose**idempotent**generated*part belongs to F,,,. ...##
###
Semidistributive inverse semigroups

2001
*
Journal of the Australian Mathematical Society
*

An inverse

doi:10.1017/s1446788700002706
fatcat:fvobjefwzrg4bgtkvjhck45w6i
*semigroup*S*is*said to be meet (join) semidistributive if its lattice .if &(S) of full inverse*subsemigroups**is*meet (join) semidistributive. ... We show that every meet (join) semidistributive inverse*semigroup**is*in fact distributive. 2000 Mathematics subject classification: primary 20M18,08A3O. use, available at https://www.cambridge.org/core ... As in the rest of the paper, if S*is*an inverse*semigroup*and X a subset of S then the inverse*subsemigroup*of S*generated*by X*is*denoted {(X)), while the full inverse*subsemigroup*that it*generates**is*...##
###
On varieties of rational languages and variable-length codes

1982
*
Journal of Pure and Applied Algebra
*

W

doi:10.1016/0022-4049(82)90005-6
fatcat:tqov4xix7re4pi753v4uwbe5e4
*generated*by all semidirect products of a monoid of V by a monoid of W, for various varieties W, and we describe the corresponding operation*on*varieties of languages. ... This article*is*a continuation of the work of the second author*on*the connections between the theory of varieties of languages and the theory of codes. ... If e=0, then e~ -1 = {0}*is**aperiodic*. If e= 1, then l~u -I*is*the*subsemigroup*of R*generated*by a and thus l~u -l*is**aperiodic*. ...##
###
The q-theory of finite semigroups: history and mathematics
[article]

2014
*
arXiv
*
pre-print

This paper

arXiv:1409.2308v2
fatcat:f6awhe4vjbg5jmxobgrtj3sifi
*is*a historical and mathematical review of the book, "The q-theory of Finite*Semigroups*" by John Rhodes and Benjamin Steinberg. ... Section 4.13 gives the first book version of Graham's Theorem [21]*on*the structure of the*idempotent**generated**subsemigroup*of a completely 0-simple*semigroup*. ... Less well known are the type I*subsemigroups*of a finite*semigroup*S. These are the analogue of the type II*subsemigroup*with respect to relational morphisms to*aperiodic**semigroups*. ...##
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E-local pseudovarieties

2012
*
Semigroup Forum
*

*Generalizing*a property of the pseudovariety of all

*aperiodic*

*semigroups*observed by Tilson, we call E-local a pseudovariety V which satisfies the following property: for a finite

*semigroup*, the

*subsemigroup*...

*generated*by its

*idempotents*belongs to V if and only if so do the

*subsemigroups*

*generated*by the

*idempotents*in each of its regular D-classes. ... This work

*is*part of the author's doctoral thesis, written under the supervision of Prof. Jorge Almeida, from

*whose*advice the author has greatly benefited. ...

##
###
Page 5531 of Mathematical Reviews Vol. , Issue 87j
[page]

1987
*
Mathematical Reviews
*

*On*the other hand, L(S)

*is*weakly modular if and only if S

*is*a rectangular group

*whose*maximal subgroups have modular subgroup lattices. ... The author characterizes

*semigroups*which satisfy the following property P: Each monogenic

*subsemigroup*

*is*normal. ...

##
###
Infinite iteration of matrix semigroups II. Structure theorem for arbitrary semigroups up to aperiodic morphism

1986
*
Journal of Algebra
*

*is*the

*subsemigroup*of S" (direct power) consisting of all those functions K + S

*whose*range

*is*,finitr. ... A

*semigroup*F

*is*

*idempotent*-free iff (F, F)^AR'RI

*is*,free over F. More

*generally*, if F

*is*

*idempotent*-free then for any set of

*generators*A of Fz (F, A)^^R

*is*free over A. ... So using y,xk = y, we find, by computing: It

*is*possible to give more detailed results

*on*torsion and

*aperiodic*classes, including additional invariants, orderings and unary and binary operations

*on*the ...

##
###
Krohn--Rhodes complexity of Brauer type semigroups
[article]

2013
*
arXiv
*
pre-print

The Krohn--Rhodes complexity of the Brauer

arXiv:1202.4982v5
fatcat:ddmw64jderbs7k5cwhfwi4czqq
*semigroup*B_n and of the annular*semigroup*A_n*is*computed. ... Since SingEA 4*is**idempotent**generated*we infer that K G (A 4 ) = SingEA 4 ∪ {1} an the latter*is**aperiodic*. ... It*is*not possible to apply Proposition 3 here because SingA n*is*not*idempotent**generated*(nor contained in the type II*subsemigroup*). ...
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