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: Some older results on multiplicative bases of integers are generalized to a certain class of commutative semigroups and the structure of union bases ofintegers is examined.
Abstract: We generalize some older results on multiplicative bases of integers to a certain class of commutative semigroups. In particular, we examine the structure of union bases of integers.
2 citations
TL;DR: In this article, it was shown that every semigroup can be isomorphically embedded into a semigroup such that its diagonal bi-act of second order is cyclic, but the diagonal biact of third order is not finitely generated.
Abstract: An example of a right cancellative semigroup is constructed such that the diagonal bi-act of this semigroup is cyclic. Moreover, it is proved that every semigroup can be isomorphically embedded into a semigroup such that its diagonal bi-act of second order is cyclic, but the diagonal bi-act of third order is not finitely generated.
2 citations
TL;DR: It is proved that the semigroup of all transformations of a 3-element set with rank at most 2 does not have a finite basis of identities, which gives a negative answer to a question of Shevrin and Volkov.
Abstract: We prove that the semigroup of all transformations of a 3-element set with rank at most 2 does not have a finite basis of identities. This gives a negative answer to a question of Shevrin and Volkov. It is worthwhile to notice that the semigroup of transformations with rank at most 2 of an n-element set, where n > 4, has a finite basis of identities. A new method of constructing finite non-finitely based semigroups is developed.
2 citations
TL;DR: In this paper, the smallest cancellative fully invariant congruence for a given relation on a free semigroup was described, and a poset of corresponding varieties of groups was given.
Abstract: For a given relation $\rho$ on a free semigroup ${\mathcal F}$ we describe the smallest cancellative fully invariant congruence ${\rho}^{\sharp}$ containing $\rho$. Two semigroup identities are s-equivalent if each of them is a consequence of the other on cancellative semigroups. If two semigroup identities are equivalent on groups, it is not known if they are s-equivalent. We give a positive answer to this question for all binary semigroup identities of the degree less or equal to 5. A poset of corresponding varieties of groups is given.
2 citations
TL;DR: In this paper, the structure of the semigroup S is investigated when RS admits a compact topology and it is proved that the last principal factors of S have finitely many of right or left ideals.
Abstract: The structure of the semigroup S is investigated when the semigroup ring RS admits a compact topology. It is proved that, in case of the semisimple semigroup S , the ”last” principal factors of S have finitely many of right or left ideals. It is shown that it is not true for other factors.
2 citations