一类半环上的开算子

Congruence openings on a class of semirings

为研究一类半环上的开同余,采用格林关系和同态的方法。给出了加法半群为半格的半环上由格林关系所确定的半环上的开同余的性质,证明了由该开同余出发得到的3个不同的半环类均是簇。对加法半群为半格的半环簇的子簇格进行了研究,得到了两个开算子。所得结果对研究加法半群为半格的半环簇有着重要作用。

To study congruence openings on a class of semirings. The method of Green＇s relations and homo- morphisms is used. The properties of congruence openings of a semiring are given that is determined by Green＇ s relations of a semiring with a semilattice addictive reduct and three classes of scmirings which are obtained by means of the congruence openings are all varieties of semirings proved. And an open operator is investigated on the lattice of all subvarieties of the variety of semirings with a semilattic addictive reduct and two opening operators are obtained. The obtained results are very helpful to study varieties of semirings with a semilattice addictive reduct.