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: Barucci and Froberg as discussed by the authors characterized almost symmetric numerical semigroups by symmetry of pseudo-Frobenius numbers and gave a criterion for H� ∗ (the dual of M) to be an almost-symmetric semigroup.
Abstract: The notion of an almost symmetric numerical semigroup was given by V. Barucci and R. Froberg in J. Algebra, 188, 418–442 (1997). We characterize almost symmetric numerical semigroups by symmetry of pseudo-Frobenius numbers. We give a criterion for H
∗ (the dual of M) to be an almost symmetric numerical semigroup. Using these results we give a formula for the multiplicity of an opened modular numerical semigroup. Finally, we show that if H
1 or H
2 is not symmetric, then the gluing of H
1 and H
2 is not almost symmetric.
55 citations
TL;DR: The strong Burnside problem has an affirmative answer for semigroups of finite dimensional matrices over a skew field as discussed by the authors, and it follows that a torsion semigroup embeddable in the multiplicative semigroup of an algebra over a field satisfying a polynomial identity is locally finite.
55 citations
55 citations
01 Feb 1980
TL;DR: In this article, a property of rings that satisfies the conditions that homomorphic images of I-rings are Ir-rings and ideals of Ir-ring are ir-rings is defined.
Abstract: ABSTRACr Let qr be a property of rings that satisfies the conditions that (i) homomorphic images of I-rings are Ir-rings and (ii) ideals of Ir-rings are Ir-rings Let S be a semilattice P of semigroups S If each semigroup ring R[SG] (a E P) is IT-semisimple, then the semigroup ring R[SG] is also Ir-semisimple Conditions are found on P to insure that each R[SG] (a E P) is Ir-semisimple whenever S is a strong semilattice P of semigroups S and R[S] is Ir-semisimple Examples are given to show that the conditions on P cannot be removed These results and examples answer several questions raised by J Weissglass
55 citations
TL;DR: In this article, the authors studied algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C ( p, q ) and proved that a topological semiigroup S with pseudocompact square contains no dense copy of C( p, q ).
54 citations