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
The aim of this paper is to study regular orthocryptogroups. After obtaining some charac- terizations of such semigroups, we establish the construction theorem of regular orthocryptogroups. As an application, we give ...The aim of this paper is to study regular orthocryptogroups. After obtaining some charac- terizations of such semigroups, we establish the construction theorem of regular orthocryptogroups. As an application, we give the construction theorem of right quasi-normal orthocryptogroups and study homomorphisms between two regular orthocryptogroups.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.
基金The research is supported by NSF for youth of Shandong Province. China.
文摘The aim of this paper is to study regular orthocryptogroups. After obtaining some charac- terizations of such semigroups, we establish the construction theorem of regular orthocryptogroups. As an application, we give the construction theorem of right quasi-normal orthocryptogroups and study homomorphisms between two regular orthocryptogroups.
