Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: In this article, a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B is presented, which is weakly B-abundant and satisfies the congruence condition (C).
Abstract: The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider are weakly B-abundant and satisfy the congruence condition (C). Any orthodox semigroup S with E(S)=B lies in our class. On the other hand, if a semigroup S lies in our class, then S is Ehresmann if and only if B is a semilattice.
15 citations
TL;DR: In this paper, it was shown that the inversion of a continuous semigroup operation in a countably compact Hausdorff space is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, and (3) S is topologically regular and the square S × S is regular.
Abstract: Let S be a countably compact Hausdorff space endowed with a continuous semigroup operation turning S into an inverse semigroup. It is shown that the inversion inv : x ↦ x-1 in S is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, (3) the semigroup S is Clifford, topologically periodic and the square S × S is regular and countably compact. These results are close to the best possible since there is an example of a quasi-regular sequentially compact commutative inverse topological semigroup with discontinuous inversion.
15 citations
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TL;DR: In this paper, the authors studied the algebraic structure of the compact right-topological semigroup λ(X) consisting of maximal linked systems on a group given a group $X$ and constructed a faithful representation of this semigroup in the semigroup of all self-maps of the power set.
Abstract: Given a group $X$ we study the algebraic structure of the compact right-topological semigroup $\lambda(X)$ consisting of maximal linked systems on $X$. This semigroup contains the semigroup $\beta(X)$ of ultrafilters as a closed subsemigroup. We construct a faithful representation of the semigroup $\lambda(X)$ in the semigroup of all self-maps of the power-set of $X$ and using this representation describe the structure of minimal ideal and minimal left ideals of $\lambda(X)$ for each twinic group $X$. The class of twinic groups includes all amenable groups and all groups with periodic commutators but does not include the free group with two generators.
15 citations
TL;DR: In this article, the authors prove the κ-tameness of pseudovarieties N, D, K and LI, where κ is the signature comprising semigroup multiplication and the omega implicit operation.
Abstract: Tameness is a strong property of semigroup pseudovarieties related to the membership problem. Let κ be the signature comprising semigroup multiplication and the omega implicit operation. We prove the κ-tameness of the pseudovarieties N, D, K and LI.
15 citations
TL;DR: In this paper, a necessary and sufficient condition is given in order that a lattice-ordered semigroup admit a totally ordered l-homomorphic image (Theorem 1), which permits us to give a necessary condition that a semigroup be representable, that is, that it be l-isomorphic to a subdirect product of totally ordered semigroups.
Abstract: A necessary and sufficient condition is given in order that a lattice-ordered semigroup admit a totally ordered l-homomorphic image (Theorem 1). This permits us to give (Theorem 2) a necessary and sufficient condition that a lattice-ordered semigroup be representable, that is, that it be l-isomorphic to a subdirect product of totally ordered semigroups, thereby solving a problem posed by L. Fuchs ([2], p. 289). We also establish a necessary and sufficient condition that a semigroup be an o-semigroup, that is, that it admit a structure of totally ordered semigroup (Theorem 3).
15 citations