A semigroup （S, .） is called right （left） quasiresiduated if for any a, b in S there exists x in S such that ax≤s b （xa≤s b） with respect to the natural partial order ≤s of S. This concept has its origin in t...A semigroup （S, .） is called right （left） quasiresiduated if for any a, b in S there exists x in S such that ax≤s b （xa≤s b） with respect to the natural partial order ≤s of S. This concept has its origin in the theory of residuated semigroups, but can also be seen as a generalization of the right （left） simplicity of semigroups. It is first studied for totally-, resp., trivially-ordered semigroups, and then for semigroups with idempotents. In particular, the cases when （S≤s） is directed downwards and when S contains a zero （with respect to a more restrictive definition） are dealt with. Throughout, examples are given; in total, 30 classes of （often well-known） semigroups of this kind are specified.展开更多
文摘A semigroup （S, .） is called right （left） quasiresiduated if for any a, b in S there exists x in S such that ax≤s b （xa≤s b） with respect to the natural partial order ≤s of S. This concept has its origin in the theory of residuated semigroups, but can also be seen as a generalization of the right （left） simplicity of semigroups. It is first studied for totally-, resp., trivially-ordered semigroups, and then for semigroups with idempotents. In particular, the cases when （S≤s） is directed downwards and when S contains a zero （with respect to a more restrictive definition） are dealt with. Throughout, examples are given; in total, 30 classes of （often well-known） semigroups of this kind are specified.
