关于一类半环的研究

On a class of semirings

借助半环的同态定理和乘法半群的格林关系,引入并研究乘法半群满足xn+1≈x的半环上由格林关系所确定的开同余,证明由开同余出发得到的半环类都是簇。借助闭算子的定义,对乘法半群为纯正密码群且满足xn+1≈x的半环所作成的半环簇[xn+1≈x]∩OBG的子簇格进行探讨。研究半环簇[xn+1≈x]∩OBG的一些子簇。

Congruence openings determined by Green＇s relations of a semiring whose multiplicative semigroup satisfies x^n ＋ 1≈x is introduced and studied by using semiring the homomorphisms theorem and Green＇s relations on the multiplicative semigroup of a semiring. Firstly,it is shown that any classe of semirings which are obtained by the congruence openings is variety. Secondly,it is investigated that the lattice of all subvarieties of the variety [x^n ＋ 1≈x]∩OBG of semirings whose multiplicative semigroups are orthocryptogroups and satisfy by the definition of closure operator. Finally,some subvarieties of the semiring variety [x^n ＋ 1≈x]∩OBG are studied.