Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
Papers published on a yearly basis
Papers
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TL;DR: An automorphism Φ of a semigroup S is said to be an inner automomorphism if there exists a unit u in S such that for each a in S, u in U can be replaced by another unit in S.
Abstract: An automorphism Φ of a semigroup S is said to be an inner automorphism if there exists a unit u in S such that for each a in S.
11 citations
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11 citations
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TL;DR: In this article, the amenability of the semigroup algebras is investigated, where a group congruence (not necessarily minimal) on a semigroup S is defined.
Abstract: We investigate the amenability of the semigroup algebras \({\ell^1(S/\rho)}\) , where \({\rho}\) is a group congruence (not necessarily minimal) on a semigroup S. We relate this to a new notion of amenability of Banach algebras modulo an ideal, to prove a version of Johnson’s theorem for a large class of semigroups, including inverse semigroups, E-inversive semigroup and E-inversive E-semigroups.
11 citations
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TL;DR: In this article, it was shown that for a large class of countably infinite abelian semigroups, there exists a basis whose representation function is exactly equal to the given function for every element in the semigroup.
Abstract: A subset of an abelian semigroup is called an asymptotic basis
for the semigroup if every element of the semigroup with at most
finitely many exceptions can be represented as the sum of two
distinct elements of the basis. The representation function of
the basis counts the number of representations of an element of
the semigroup as the sum of two distinct elements of the basis.
Suppose there is given function from the semigroup into the set
of nonnegative integers together with infinity such that this
function has only finitely many zeros. It is proved that for a large class of countably infinite
abelian semigroups, there exists a basis whose representation
function is exactly equal to the given function for every
element in the semigroup.
11 citations