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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 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.  ... 
doi:10.1142/s021819670400202x fatcat:5hcettoqbnbibmrne6fp5fbidy

On a problem of M. P. Schützenberger

D. B. McAlister
1980 Proceedings of the Edinburgh Mathematical Society  
If D e *& then, as pointed out by Schiitzenberger, the 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.  ... 
doi:10.1017/s0013091500003795 fatcat:5wceykozozcmlgemwlr4zpcjta

Inverse semigroups determined by their lattices of convex inverse subsemigroups II

Kyeong Hee Cheong, Peter R. Jones
2003 Algebra Universalis  
For some slightly narrower classes it 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.  ... 
doi:10.1007/s000120300004 fatcat:jxm3o4d2v5hznerk45qf5pgkbm

Finite aperiodic semigroups with commuting idempotents and generalizations

Peter M. Higgins, Stuart W. Margolis
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?  ... 
doi:10.1007/bf02773226 fatcat:ghibli7p7bakvnk7xu4o336z4i


2004 Glasgow Mathematical Journal  
An L-isomorphism between inverse 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.  ... 
doi:10.1017/s0017089503001666 fatcat:i3yc6j2q55ayzde45o6my2coli

Covers for regular semigroups and an application to complexity

P.G. Trotter
1995 Journal of Pure and Applied Algebra  
It 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  ... 
doi:10.1016/0022-4049(94)00151-0 fatcat:7pczhyf4ara23m2n7pdg7qyara


2008 Glasgow Mathematical Journal  
NOS = EI m POI and NOS ∩ A = N m POI, where A, EI and N denote the pseudovarieties of all 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.  ... 
doi:10.1017/s0017089508004230 fatcat:p6qk4kxidnectb4k6s57gzfvgm

Page 40 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
to E; the greatest idempotent separating congruence onis 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

Katherine G. Johnston-Thom, Peter R. Jones
2001 Journal of the Australian Mathematical Society  
An inverse 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  ...  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  ... 
doi:10.1017/s1446788700002706 fatcat:fvobjefwzrg4bgtkvjhck45w6i

On varieties of rational languages and variable-length codes

Jean-Eric Pin
1982 Journal of Pure and Applied Algebra  
W 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.  ... 
doi:10.1016/0022-4049(82)90005-6 fatcat:tqov4xix7re4pi753v4uwbe5e4

The q-theory of finite semigroups: history and mathematics [article]

Stuart W. Margolis
2014 arXiv   pre-print
This paper 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.  ... 
arXiv:1409.2308v2 fatcat:f6awhe4vjbg5jmxobgrtj3sifi

E-local pseudovarieties

A. Moura
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.  ... 
doi:10.1007/s00233-012-9413-3 fatcat:hiba5whhungatbgcz6vsy3pozi

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

John Rhodes
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  ... 
doi:10.1016/0021-8693(86)90070-0 fatcat:rmx2zqgsyvg3jlr33pvx7hfgfy

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

Karl Auinger
2013 arXiv   pre-print
The Krohn--Rhodes complexity of the Brauer 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).  ... 
arXiv:1202.4982v5 fatcat:ddmw64jderbs7k5cwhfwi4czqq
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