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E-INVERSIVE *-SEMIGROUPS

Shoufeng Wang, Yinghui Li
2012 Communications of the Korean Mathematical Society  
In this paper, E-inversive * -semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.  ...  A unary semigroup (S, * ) is called an E-inversive * -semigroup if the following identities hold: x * xx * = x * , (x * ) * = xx * x, (xy) * = y * x * .  ...  E-inversive * -semigroups are E-inversive from the first identity above. On the other hand, E-inversive * -semigroups form a variety of unary semigroups, denoted by E * .  ... 
doi:10.4134/ckms.2012.27.4.689 fatcat:fik37gg2wzckbio7uu6pmruzt4

E-Inversive Γ-Semigroups

Mridul Kanti Sen, Sumanta Chattopadhyay
2009 Kyungpook Mathematical Journal  
In this paper we investigate different properties of E-inversive Γ-semigroup and right E-Γ-semigroup.  ...  A Γ-semigroup S is called an E-inversive Γ-semigroup if for each a ∈ S there exist x ∈ S and α ∈ Γ such that aαx is a β-idempotent for some β ∈ Γ.  ...  not be an E * -inversive semigroup for some α ∈ Γ, but S may be an E * -inversive Γ-semigroup.  .  ... 
doi:10.5666/kmj.2009.49.3.457 fatcat:3fgjiexzxzaczh5iqhuzblacry

The geometric theory of inverse semigroups I: E-unitary inverse semigroups

M.V. Lawson
1990 Journal of Pure and Applied Algebra  
The consequences of this approach for the theory of E-unitary covers of inverse semigroups and its generalisations are worked out in subsequent papers.  ...  We show how the correspondence between inverse semigroups and inductive groupoids (a class of ordered groupoids) leads to a reinterpretation of McAlister's P-Theorem as a function extension theorem.  ...  Thus e@f =er\f. Whence S(G) is an inverse semigroup; the semigroup inverse of an element x is just x-' , the inverse in the groupoid.  ... 
doi:10.1016/0022-4049(90)90011-6 fatcat:iebw67ziz5cw3anynxq2wdmwuy

E-solid locally inverse semigroups [article]

Tamás Dékány, Mária B. Szendrei, István Szittyai
2018 arXiv   pre-print
We prove that if S is an E-solid locally inverse semigroup, and ρ is an inverse semigroup congruence on S such that the idempotent classes of ρ are completely simple semigroups then S is embeddable into  ...  Consequently, the E-solid locally inverse semigroups turn out to be, up to isomorphism, the regular subsemigroups of λ-semidirect products of completely simple semigroups by inverse semigroups.  ...  E-solid locally inverse semigroups.  ... 
arXiv:1807.01265v1 fatcat:sofbgqvkgfg2dci5t7midrxbza

Strongly E-reflexive inverse semigroups

L. O'Carroll
1977 Proceedings of the Edinburgh Mathematical Society  
In fact, we show that an inverse semigroup is strongly E-reflexive if and only if it is a semilattice of E-unitary inverse semigroups.  ...  Thus an E-unitary inverse semigroup is strongly E-reflexive, and a strongly E-reflexive inverse semigroup is E-reflexive. As shown below, neither of these statements can be reversed.  ...  E-unitary inverse semigroups.  ... 
doi:10.1017/s0013091500026584 fatcat:msb5khatibdcfpxfsgmuak7jmy

E-unitary inverse semigroups over semilattices

D. B. McAlister
1978 Glasgow Mathematical Journal  
An inverse semigroup is called E-unitary if the equations ea = e = e 2 together imply a 2 = a.  ...  Let S be an inverse semigroup. Then we say that S is an E-unitary inverse semigroup over a semilattice if S = P(G, 26, "3/) for some triple (G, 26, "30 with SC a semilattice.  ...  Let S be an inverse semigroup and let e, / be idempotents of S.  ... 
doi:10.1017/s0017089500003311 fatcat:5nsd57ea4baz3j34pifhv2k2nu

E-unitary covers for inverse semigroups

D. B. McAlister, Norman Reilly
1977 Pacific Journal of Mathematics  
An inverse semigroup is called E -unitary if the equations ea = e = e 2 together imply a 2 = a. In a previous paper, the first author showed that every inverse semigroup has an E unitary cover.  ...  That is, if S is an inverse semigroup, there is an E unitary inverse semigroup P and an idempotent separating homomorphism of P onto S.  ...  E~unitary covers. An inverse semigroup is called Eunitary if the equations ea = e = e 2 together imply a 2 = a.  ... 
doi:10.2140/pjm.1977.68.161 fatcat:2djclsl3wfbztkfh6p7msycgsq

E-unitary congruences on inverse semigroups

N. R. Reilly, W. D. Munn
1976 Glasgow Mathematical Journal  
By an £"-unitary inverse semigroup we mean an inverse semigroup in which the semilattice is a unitary subset.  ...  A congruence p on an inverse semigroup S is called an /T-unitary congruence if and only if S/p is an ^-unitary inverse semigroup.  ...  be called an E-unitary inverse semigroup.  ... 
doi:10.1017/s0017089500002731 fatcat:j4fjbmjqsnatnp6aaiq6gbxbmi

Strongly E-reflexive inverse semigroups II

L. O'Carroll
1978 Proceedings of the Edinburgh Mathematical Society  
This class was shown to coincide with the class of those inverse semigroups which are semilattices of E-unitary inverse semigroups.  ...  Let S be an inverse semigroup with semilattice of idempotents E. Let a = {(*, y) £ S x S\ex -ey for some e G E}; then a is the minimum group congruence on S (10).  ...  Then S is strongly E-reflexive if and only if S is a subdirect product of E-unitary inverse semigroups and E-unitary inverse semigroups with zero. Proof. Suppose that 5 is strongly E-reflexive.  ... 
doi:10.1017/s0013091500015819 fatcat:iofo2feesvff5oyvicbwvtjuua

Subdirect products of E–inversive semigroups

H. Mitsch
1990 Journal of the Australian Mathematical Society  
A semigroup S is called .E-inversive if for every a € S there is an x € S such that (ax) 1 = ax.  ...  For this purpose, the explicit form of the least group congruence on an arbitrary .E-inversive semigroup is given.  ...  THEOREM Let S be an E-inversive semigroup, Gbea group and P be an E-inversive, E-unitary cover ofS through G.  ... 
doi:10.1017/s1446788700035199 fatcat:oyvqrmmcw5dbxgvlpxjk3db3te

Bands of E-Inversive Unipotent Semigroups

Roman S. Gigoń
2019 Bulletin of the Malaysian Mathematical Sciences Society  
We study some special types of bands of E-inversive unipotent semigroups.  ...  It has been proved that in any R-semigroup S, which is a band of E-inversive unipotent semigroups, the set of its regular elements is a retract of S.  ...  Proof Indeed, each G e is a unipotent (E-inversive) semigroup, so S/θ is the band S/ρ of the unipotent (E-inversive) semigroups G e (eE S ).  ... 
doi:10.1007/s40840-019-00835-4 fatcat:32akphpswjhbbekp6fmjcnhh4a

Generalised domain and E-inverse semigroups

Tim Stokes
2018 Semigroup Forum  
A generalised D-semigroup is here defined to be a left E-semiabundant semigroup S in which the R E -class of every x ∈ S contains a unique element D(x) of E, made into a unary semigroup.  ...  A generalisation of inverse semigroups in which inverses are defined relative to a set of idempotents arises as a special case, and a finite equational axiomatisation of the resulting unary semigroups  ...  Examples 2.16 and 3.9 were both obtained with the aid of Mace4, and the proof that generalised D-semigroups form a variety was obtained with the assistance of Prover9.  ... 
doi:10.1007/s00233-018-9917-6 fatcat:slko6ldrlfhvxnhrbcg6fuxyqe

The geometric theory of inverse semigroups II: E-unitary covers of inverse semigroups

Mark V. Lawson
1992 Journal of Pure and Applied Algebra  
., The geometric theory of inverse semigroups II: E-unitary covers of inverse semigroups, Journal of Pure and Applied Algebra 83 (1992) 121-139.  ...  As an application. we show that the category of E-unitary covers of an inverse semigroup is equivalent to a category of embeddings into generalisations of factorisable inverse monoids.  ...  A further example is provided by our treatment of the well-known relationship between E-unitary covers of an inverse semigroup S and embeddings of S into factorisable inverse monoids [ 13).  ... 
doi:10.1016/0022-4049(92)90159-d fatcat:et76jqu6hzblxdwt3mbwl3fa6y

Weakly E-unitary locally inverse semigroups

Bernd Billhardt, Mária B. Szendrei
2003 Journal of Algebra  
We prove that each weakly E-unitary locally inverse semigroup is embeddable in a restricted semidirect product of a normal band by a completely simple semigroup and, equivalently, in a Pastijn product  ...  of a normal band by a completely simple semigroup.  ...  Consequently, K T is a weakly E-unitary locally inverse semigroup.  ... 
doi:10.1016/s0021-8693(03)00395-8 fatcat:cpq5ejtgzrefvb2mzqd3wjzlom

On E-solid Semigroups with Inverse Transversals

Limin Wang
2001 Southeast Asian Bulletin of Mathematics  
We characterize E-solid semigroups with inverse transversals and some special such semigroups in terms of congruences.  ...  Some properties of inverse congruences over completely simple semigroups are obtained.  ...  Let S be a regular semigroup. An inverse subsemigroup S of S is called an inverse transversal if S contains an unique inverse x for each x e S.  ... 
doi:10.1007/s10012-001-0335-3 fatcat:kbngxgwvizeyxfgrxw2htwypx4
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