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2007•Basic Sciences Journal of Textile UniversitiesRequires access

Properties and characterizations of a class of quasi-regular semigroups

Siyao Ma

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Abstract

A class of quasi-regular semigroup is defined,namely quasi-right semigroup.By using properties of quasi-regular semigroups and left central idempotents,some statements are proved.Let S be a quasi-right semigroup,then(1) S is a quasi-completely regular semigroup;(2) RegS is a completely regular semigroup;(3) R* is the smallest semilattice congruence on S;(4) Each R-class Tα on RegS is a right group;(5) TαGα×Eα,where Gα is a group,Eα is a right zero semigroup.On the basis,three equivalent statements are obtained.Let S be a semigroup with left central idempotents,then (1) S is a quasi-right semigroup;(2) S is a quasi-completely regular,and RegS is an ideal;(3) S is a nil-extension of strong semilattice of right semigroup.

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A class of quasi-regular semigroup is defined,namely quasi-right semigroup.By using properties of quasi-regular semigroups and left central idempotents,some statements are proved.Let S be a quasi-right semigroup,then(1) S is a quasi-completely regular semigroup;(2) RegS is a completely regular semigroup;(3) R* is the smallest semilattice congruence on S;(4) Each R-class Tα on RegS is a right group;(5) TαGα×Eα,where Gα is a group,Eα is a right zero semigroup.On the basis,three equivalent statements are obtained.Let S be a semigroup with left central idempotents,then (1) S is a quasi-right semigroup;(2) S is a quasi-completely regular,and RegS is an ideal;(3) S is a nil-extension of strong semilattice of right semigroup.

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Available abstract

A class of quasi-regular semigroup is defined,namely quasi-right semigroup.By using properties of quasi-regular semigroups and left central idempotents,some statements are proved.Let S be a quasi-right semigroup,then(1) S is a quasi-completely regular semigroup;(2) RegS is a completely regular semigroup;(3) R* is the smallest semilattice congruence on S;(4) Each R-class Tα on RegS is a right group;(5) TαGα×Eα,where Gα is a group,Eα is a right zero semigroup.On the basis,three equivalent statements are obtained.Let S be a semigroup with left central idempotents,then (1) S is a quasi-right semigroup;(2) S is a quasi-completely regular,and RegS is an ideal;(3) S is a nil-extension of strong semilattice of right semigroup.

Key concepts: Semilattice, Semigroup, Mathematics, Ideal (ethics), Cancellative semigroup, Congruence (geometry), Class (philosophy), Regular semigroup

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