半环的格林关系所确定的半环簇

Semiring varieties defined by Green’s relations on a semiring

给出了由半环的格林关系所确定的开同余的刻画与性质。通过这些开同余,得到了系列半环类,证明了这些半环类均是半环簇,并揭示了这些半环簇之间的关系。通过对半环簇的子簇格上的开算子的探究,得到了乘法幂等半环簇的子簇格到开簇格的直积上的序嵌入定理。

The properties and characterizations of congruence openings determined by Green’s relations of a semiring are given. We obtain that several classes of semirings by means of these congruence openings,prove that these classes of semirings are varieties of semirings,and uncover relationships between these varieties. By exploring opening operators on the lattice of all subvarieties of varieties of semirings,the order embedding theorem of the lattice of all subvarieties of the variety of multiplicatively idempotent semirings into the direct product of the lattice of open varieties is given.