4,463 research outputs found
On finite complete rewriting systems and large subsemigroups
Let be a semigroup and be a subsemigroup of finite index in (that
is, the set is finite). The subsemigroup is also called a
large subsemigroup of . It is well known that if has a finite complete
rewriting system then so does . In this paper, we will prove the converse,
that is, if has a finite complete rewriting system then so does . Our
proof is purely combinatorial and also constructive.Comment: We have made major changes to the paper and simplified most of the
proof
On semigroups of endomorphisms of a chain with restricted range
Let be a finite or infinite chain and let be the monoid of all
endomorphisms of . In this paper, we describe the largest regular
subsemigroup of and Green's relations on . In fact, more
generally, if is a nonempty subset of and the subsemigroup of
of all elements with range contained in , we characterize the largest
regular subsemigroup of and Green's relations on . Moreover,
for finite chains, we determine when two semigroups of the type are
isomorphic and calculate their ranks.Comment: To appear in Semigroup Foru
Generalized Green'S Equivalences on the Subsemigroups of the Bicyclic Monoid
We study generalized Green's equivalences on all subsemigroups of the bicyclic monoid B and determine the abundant (and adequate) subsemigroups of B. © 2010 Copyright Taylor and Francis Group, LLC
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