The matrix envelope of a semigroup
Copyright policy )The matrix envelope of a semigroup
The purpose of this paper is to faithfully represent a semigroup S which satisfies DCC on both left and right ideals by row-monomial matrices over a group with zero. If there are only finitely many left ideals and right ideals then the matrices are finite. \{Reviewer's remark: the representation is a direct sum of three distinct representations. Whilst two of these are indeed by row-monomial matrices, the third is in fact by column-monomial matrices. Transposing the matrices unfortunately leads to an anti-representation in that case.\}
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Semigroups of transformations, relations, partitions, etc., group with zero, Algebra and Number Theory, Representation of semigroups; actions of semigroups on sets, matrix representation, row-monomial matrices
Semigroups of transformations, relations, partitions, etc., group with zero, Algebra and Number Theory, Representation of semigroups; actions of semigroups on sets, matrix representation, row-monomial matrices
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