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
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
By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completel...By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J*,^-simple semigroups. The result generalizes Petrich’s result on completely regular semigroups with Green’s relation H a normal band congruence or a regular band congruence from the round of regular semigroups to the round of r-ample semigroups.展开更多
基金This work is supported by the Natural Science Foundation of Jiangxi Provincethe Science Foundation of Education Department of Jiangxi Province and also by the Foundation of Jiangxi Normal University.
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.
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.
文摘By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J*,^-simple semigroups. The result generalizes Petrich’s result on completely regular semigroups with Green’s relation H a normal band congruence or a regular band congruence from the round of regular semigroups to the round of r-ample semigroups.
