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 paper, it was shown that if a semigroup variety is an upper-modular element of this lattice and different from the variety of all semigroups then it is a periodic variety and every nilsemigroup in the variety is commutative and satisfies the identity x2y = xy2.
Abstract: We completely determine all commutative semigroup varieties that are upper-modular elements of the lattice of all semigroup varieties. It is verified that if a semigroup variety is an upper-modular element of this lattice and different from the variety of all semigroups then it is a periodic variety and every nilsemigroup in the variety is commutative and satisfies the identity x2y = xy2.
32 citations
32 citations
TL;DR: In this paper, it is shown that the isomorphy classes of the ideals of a valuation domain form a Clifford semigroup, and the structure of this semigroup is investigated.
Abstract: It is shown that the isomorphy classes of the ideals of a valuation domain form a Clifford semigroup, and the structure of this semigroup is investigated. The group constituents of this Clifford semigroup are exactly the quotients of totally ordered complete abelian groups, modulo dense subgroups. A characterization of these groups is obtained, and some realization results are proved when the skeleton of the totally ordered group is given.
31 citations
01 Sep 1997
TL;DR: The aim of this paper is to present algorithms to compute finite semigroups, given by a set of generators taken in a larger semigroup, called the “universe”.
Abstract: The aim of this paper is to present algorithms to compute finite semigroups. The semigroup is given by a set of generators taken in a larger semigroup, called the “universe”. This universe can be for instance the semigroup of all functions, partial functions, or relations on the set , or the semigroup of × n matrices with entries in a given finite semiring.
31 citations
TL;DR: In this paper, a covering theorem of McAlister type is obtained for banded and free guarded semigroups, and a canonical forgetful functor from guarded semigroup to banded semigroup is given.
Abstract: The variety of guarded semigroups consists of all (S,·, ¯) where (S,·) is a semigroup and x ↦ \overline{x} is a unary operation subject to four additional equations relating it to multiplication. The semigroup Pfn(X) of all partial transformations on X is a guarded semigroup if x \overline{f} = x when xf is defined and is undefined otherwise. Every guarded semigroup is a subalgebra of Pfn(X) for some X. A covering theorem of McAlister type is obtained. Free guarded semigroups are constructed paralleling Scheiblich's construction of free inverse semigroups. The variety of banded semigroups has the same signature but different equations. There is a canonical forgetful functor from guarded semigroups to banded semigroups. A semigroup underlies a banded semigroup if and only if it is a split strong semilattice of right zero semigroups. Each banded semigroup S contains a canonical subsemilattice g⋆(S). For any given semilattice L, a construction to synthesize the general banded semigroup S with g⋆ ≅ L is obtained.
31 citations