Showing papers on "Bicyclic semigroup published in 1983"

Unbounded fan-in circuits and associative functions

Abstract: We consider the computation of finite semigroups using unbounded fan-in circuits. There are constant-depth, polynomial size circuits for semigroup product iff the semigroup does not contain a nontrivial group as a subset. In the case that the semigroup in fact does not contain a group, then for any primitive recursive function f, circuits of size O(nf−1(n)) and constant depth exist for the semigroup product of n elements. The depth depends upon the choice of the primitive recursive function f. The circuits not only compute the semigroup product, but every prefix of the semigroup product. A consequence is that the same bounds apply for circuits computing the sum of two n-bit numbers.

Rees matrix covers for locally inverse semigroups

Abstract: BYD. B. MCALISTERAbstract. A regular semigroup S is locally inverse if each local submonoid eSe, ean idempotent, is an inverse semigroup. It is shown that every locally inversesemigroup is an image of a regular Rees matrix semigroup, over an inversesemigroup, by a homomorphism 0 which is one-to-one on each local submonoid;such a homomorphism is called a local isomorphism. Regular semigroups which arelocally isomorphic images of regular Rees matrix semigroups over semilattices arealso characterized.

On commutative semigroup algebras

Abstract: This paper is concerned with the problem of finding necessary and sufficient conditions on a commutative semigroup S for the algebra FS of S over a field F to be semiprimitive (Jacobson semisimple).

When is the semigroup ring perfect

Abstract: A characterization of perfect semigroup rings A (G) is given by means of the properties of the ring A and the semigroup G. It was proved in (10) that for a ring with unity A and a group G the group ring A(G) is perfect if and only if A is perfect and G is finite. Some results on perfectness of semigroup rings were obtained by Domanov (3). He reduced the problem of describing perfect semigroup rings A(G) to checking that certain semigroup algebras derived from A(G) satisfy polynomial identities. Further, a characterization of such PI-algebras over a field of characteristic zero was found in (2). However, the obtained results are difficult to formulate and refer to some exterior constructions obscuring an insight into the properties of the semigroup. The purpose of this paper is to completely characterize perfect semigroup rings by means of the properties of the semigroup and the coefficient ring. Our approach is quite different from that of (3) and omits PI-methods. It works in arbitrary characteristic and the final result is a natural strengthening of the conditions for A(G) to be semilocal (7). In what follows A will be an associative ring, G-a semigroup. A is said to be

A congruence-free semigroup associated with an infinite cardinal number

Abstract: Let X be a set with infinite cardinality m and let Qm be the semigroup of balanced elements in T (X), as described by Howie. If I is the ideal {α ∈ Qm : |Xα| < m} then the Rees factor Pm = Qm/I is 0−bisimple and idempotent-generated. Its minimum non-trivial homomorphic image P ∗ m has both these properties and is congruence-free. Moreover, P ∗ m has depth 4, in the sense that [E(P ∗ m)] 4 = P ∗ m and [E(P ∗ m)] 3 6= P ∗ m.

On the singular ideals of inverse semigroup algebras

Abstract: Let FS denote the algebra of a semigroup S over a field F. Snider [3] has shown that if G is a group and F a field of characteristic 0 then the right singular ideal of FG is zero. In this note we extend his result by proving that if S is an inverse semlgroup and F a field of characteristic 0 then the right singular ideal of FS is zero. (Since an inverse semigroup has an involution, a similar result holds, of course, for the left singular ideal.)

Isomorphisms of semigroups of transformations

Abstract: If M is a centered operand over a semigroup S, the suboperands of M containing zero are characterized in terms of S-homomorphisms of M. Some properties of centered operands over a semigroup with zero are studied.