关于半环上格林关系的开同余

On congruence openings of Green′s relations on a semiring

首先给出了由半环的乘法半群上的格林关系所确定的半环开同余的性质和刻画.其次,由开同余出发,得到了六个不同的半环类,并证明了这六个半环类均是半环簇.最后,对半环簇的子簇格上的开算子进行了探讨,得到了一些有趣的结果.

In this paper we firstly give properties and characterizations of congruence openings of a semiring that is determined by Green＇s relations of multiplicative semigroup of a semiring. Secondly, we obtain six classes of semirings by means of congruence openings, and prove that these classes of semirins are all varieties of semirings. Finally, we investigate open operators on the lattice of all subvarieties of the variety of semirings and obtain some interesting results.