Showing papers on "Cancellative semigroup published in 1987"
TL;DR: In this paper, the inverse hull of a left reductive right cancellative semigroup S is represented as a quotient semigroup of the free inverse monoid generated by S. Necessary and sufficient conditions are established on S in order for its inverse hull to be E-unitary, in which case its P-representation is constructed.
11 citations
11 citations
11 citations
TL;DR: In this article, the smallest size of a set for which a finite fundamental inverse semigroup can be faithfully represented by partial transformations of that set is the number of join irreducible elements of its semilattice of idempotents.
Abstract: This paper shows that the smallest size of a set for which a finite fundamental inverse semigroup can be faithfully represented by partial transformations of that set is the number of join irreducible elements of its semilattice of idempotents.
9 citations
TL;DR: In this paper, the Jacobson radical of a semigroup ring R [S ] of a commutative semigroup S is determined when S is S -homogeneous, i.e.
7 citations
7 citations
5 citations
TL;DR: In this paper, the sum σ(e)=e+∑(−1)KeL1⋯eiK, where ei,...,em are maximal preidempotents of the idempotent e, and the summation goes over all nonempty subsets {i1,...,ik} of the set {1,...m}.
Abstract: In the semigroup algebra A of a finite inverse semigroup S over the field of complex numbers to an indempotent e there is assigned the sum σ(e)=e+∑(−1)KeL1⋯eiK, where ei,...,em are maximal preidempotents of the idempotent e, and the summation goes over all nonempty subsets {i1,...,ik} of the set {1,...m} Then for any class K of conjugate group elements of the semigroup S the element K=∑a·(a−1a) (the summation goes over all a∈g) is a central element of the algebra A, and the set {K} of all possible such elements is a basis for the center of the algebra A.
4 citations
01 Jan 1987
2 citations
01 Jan 1987
TL;DR: In this article, it was shown that if the semi-lattice of an inverse semigroup S satisfies a certain finiteness condition, introduced by Teply, Turman and Quesada in 1980, then the converse does hold.
Abstract: In 1976, Domanov showed that the algebra of an inverse semigroup S over a field F is semiprimitive (that is, has zero Jacobson radical) if the algebra of each maximal subgroup of S over F is semiprimitive. It is known that the converse statement is false in general. The principal purpose of this paper is to announce that if the semi-lattice of S satisfies a certain finiteness condition, introduced by Teply, Turman and Quesada in 1980, then the converse does hold. Corresponding results for primitivity are also discussed.
1 citations
01 Jan 1987
TL;DR: In this article, the identity element 1A of the semigroup algebra A of an arbitrary finite inverse semigroup S is presented, giving new information about how the form of 1A depends on the Vagner-Preston order in S. D. Munn and R.W. Penrose (1957) obtained an explicit formula for 1A.
Abstract: W. D. Munn and R. Penrose (1957) obtained an explicit formula for the identity element 1A of the semigroup algebra A of an arbitrary finite inverse semigroup S. An alternative (inductive) characterization of 1A is presented, giving new information about how the form of 1A depends on the Vagner-Preston order in S.