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: It is shown that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup.
Abstract: We show that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup
12 citations
TL;DR: In this paper, it was shown that any regular semigroup is a homomorphic image of a regular semiigroup whose least full self-conjugate subsemigroup is unitary; the homomorphism is injective on the sub-semigroup.
12 citations
TL;DR: A finite semigroup associated with a conjugacy class of a word in the free monoid over a finite alphabet is introduced and results on combinatorics on words are derived.
Abstract: We introduce a finite semigroup associated with a conjugacy class of a word in the free monoid over a finite alphabet. Using properties of this semigroup we derive results on combinatorics on words.
12 citations
TL;DR: A sufficient condition under which a semigroup admits no finite identity basis has been recently suggested in a joint paper by Karl Auinger, Yuzhu Chen, Xun Hu, Yanfeng Luo, and the author as mentioned in this paper.
Abstract: A new sufficient condition under which a semigroup admits no finite identity basis has been recently suggested in a joint paper by Karl Auinger, Yuzhu Chen, Xun Hu, Yanfeng Luo, and the author. Here we apply this condition to show the absence of a finite identity basis for the semigroup \(\mathrm {UT}_3(\mathbb {R})\) of all upper triangular real \(3\times 3\)-matrices with 0 s and/or 1 s on the main diagonal. The result holds also for the case when \(\mathrm {UT}_3(\mathbb {R})\) is considered as an involution semigroup under the reflection with respect to the secondary diagonal.
12 citations
TL;DR: It was shown in this paper that every finite inverse semigroup having only solvable subgroups has no finite basis of identities, unless it is a strict inverse semi-convex semigroup.
Abstract: It is shown that every finite inverse semigroup having only solvable subgroups,viewed as a semigroup with the additional unary operation of inversion, has nofinite basis of identities, unless it is a strict inverse semigroup.
12 citations