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Limin Wang 《Southeast Asian Bulletin of Mathematics》2001,25(2):335-344
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.1991 MR Subject Classification: 20M10This work was supported by the Natural Science Foundation of Guangdong, China. 相似文献
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Let S be a regular semigroup. An inverse subsemigroup S of S is called an inverse transversal if So contains an unique inverse x" for each x E S. In this case, I ~ {e E E(S)lee = e}and A = {g 6 E(S)gg = g}, are left and right regular subbands of S, respectively, where E(S)denotes the set of idempotehts in S. Denote E' = E(S). A regular semigroup S is calledE-solid if R|E(S) o LIE(S) = LIE(S) o R|E(s). A regular semigroup S is E-solid if and only ifthere is an inverse congruence… 相似文献
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We first consider an ordered regular semigroup S in which every element has a biggest inverse and determine necessary and sufficient conditions for the subset S ○ of biggest inverses to be an inverse transversal of S. Such an inverse transversal is necessarily weakly multiplicative. We then investigate principally ordered regular semigroups S with the property that S ○ is an inverse transversal. In such a semigroup we determine precisely when the set S ☆ of biggest pre-inverses is a subsemigroup and show that in this case S ☆ is itself an inverse transversal of a subsemigroup of S. The ordered regular semigroup of 2 × 2 boolean matrices provides an informative illustrative example. The structure of S, when S ☆ is a group, is also described. 相似文献
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It is dedicated to the study of inverse wrpp semigroup, we obtain some charac- terizations of inverse wpp semigroup. In particular, we establish some charactizations for C-wrpp semigroup. 相似文献
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Zhenji Tian 《代数通讯》2013,41(6):1824-1833
An inverse semigroup S is said to be 0-semidistributive if its lattice ?F (S) of full inverse subsemigroups is 0-semidistributive. We show that it is sufficient to study simple inverse semigroups which are not groups. Our main theorem states that such a simple inverse semigroup S is 0-semidistributive if and only if (1) S is E-unitary, (2) S is aperiodic, (3) for any a,b ∈ S/σ with ab ≠ 1, there exist nonzero integers n and m such that (ab) m = a n or (ab) m = b n , where σ is the minimum group congruence on S. 相似文献
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Peter R. Jones 《Semigroup Forum》2006,73(3):330-344
A lattice isomorphism between inverse semigroups S and T is an isomorphism between their lattices of inverse subsemigroups.
When S is combinatorial, it has long been known that a bijection is induced between S and T. Various authors have introduced
successively weaker "archimedean" hypotheses under which this bijection is necessarily an isomorphism, naturally inducing
the original lattice isomorphism. Since lattice-isomorphic groups need not have the same cardinality, extending these techniques
to the non-combinatorial case requires some means of tying the subgroups to the rest of the semigroup. Ershova showed that
if S has no nontrivial isolated subgroups (subgroups that form an entire D-class) then again a bijection exists between S
and T. Recently, this technique has been successfully exploited, by Goberstein for fundamental inverse semigroups and by
the author for completely semisimple inverse semigroups, under two different finiteness hypotheses. In this paper, we derive
further properties of Ershova's bijection(s) and formulate a "quasi-connected" hypothesis that enables us to derive both Goberstein's
and the author's earlier results as corollaries. 相似文献
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It is well known that the free group on a non-empty set can be totally ordered and, further, that each compatible latttice ordering on a free group is a total ordering. On the other hand, Saitô has shown that no non-trivial free inverse semigroup can be totally ordered. In this note we show, however, that every free inverse monoid admits compatible lattice orderings which are closely related to the total orderings on free groups.These orderings are natural in the sense that the imposed partial ordering on the idempotents coincides with the natural partial ordering. For this to happen in a lattice ordered inverse semigroup, the idempotents must form a distributive lattice. The method of construction of the lattice orderings on free inverse monoids can be applied to show that naturally lattice ordered inverse semigroups with a given distributive lattice E of idempotents can have arbitrary Green's relation structure. Analogous results hold for naturally -semilatticed inverse semigroups. In this case, there is no restriction on the semilattice E of idempotents.We also show that every compatible lattice ordering on the free monogenic inverse monoid is of the type considered here. This permits us to prove that there are precisely eight distinct compatible lattice orderings on this semigroup. They belong to two families, each of which contains four members, of conjuguate lattice orderings. 相似文献
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We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free
countably compact topological inverse semigroups. 相似文献
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Recently, Billhardt has characterized the locally
inverse semigroups embeddable in Rees matrix semigroups
over generalized inverse semigroups. We prove here that
these semigroups are just the locally inverse semigroups
having weakly E-unitary covers. 相似文献
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Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S. 相似文献
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A transformation semigroup over a set X with N elements is said to be a near permutation semigroup if it is generated by a group G of permutations on N elements and by a set H of transformations of rank N - 1. In this paper we give necessary and sufficient conditions for a near permutation semigroup S = ‹G,H›, where H is a group, to be inverse. Moreover, we obtain conditions which guarantee that its semilattice of idempotents is generated by the idempotents of S of rank greater than N - 2 or N - 3. 相似文献
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Vitor H. Fernandes 《Semigroup Forum》1998,56(3):418-433
NO of all normally ordered inverse semigroups. We show that the pseudovariety of inverse semigroups PCS generated by all semigroups of injective and order partial transformations on a finite chain consists of all aperiodic elements
of NO . Also, we prove that NO is the join pseudovariety of inverse semigroups. PCS V G , where G is the pseudovariety of all finite groups. 相似文献
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Oleg Gutik 《Semigroup Forum》2000,60(2):243-252
A locally compact commutative band with open principal ideals is a zero-dimensional scattered space. Cardinal invariants of locally compact and compact commutative bands with open principal ideals is investigated. A base of the topology of a compact commutative band with open principal ideals is determined and the structure of such compact semilattices in which every principal lower set is a chain is described. Every first countable compact inverse semigroup with open right (left, two-sided) principal ideals is metrizable 相似文献
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For an inverse semigroup S,the set L(S)of all inverse subsemigroups(including the empty set)of S forms a lattice with respect to intersection denoted as usual by ∩ and union,where the union is the inverse subsemingroup generated by inverse subsemigroups A,B of S.The set 相似文献
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Let S be an inverse semigroup and rho an idempotent separating congruence on S . It is proved that S can be embedded into a lambda-semidirect product of a group F by S /rho where F belongs to the variety generated by the idempotent classes of rho. 相似文献
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Research supported by NSERC. 相似文献