导　　师： 方捷

学科专业： G0101

授予学位： 硕士

作　　者： ;

机构地区： 汕头大学

摘　　要： 在本硕士论文中，首先研究了具有heyting结构的ockham代数(l；∧，∨，→，f，0，1)。其中(l；∧，∨，f，0，1)是ockllam代数，(l；∧，∨，→，0，1)是heyting代数，而且运算f和→满足f(x→y)=f2(x)∧f(y)和f(x)→y=f2(x)∨y。简称这种代数为ho-代数。发现ho-代数l的同余格conl同构于余核滤子格ckf(l)。还得出，如果l是*-半单纯次直不可约的ho-代数，那么它只有两个互不同构的次直不可约代数，并且对它们进行了详细的刻画。
　　 还研究了bdpo-代数即平衡半伪补ockham代数的滤子。bdpo-代数是一个<2，2，1，1，0，0)类型的代数(l；∧，∨，f，*，0，1)．其中(l；f)是ockham代数，(l；*)是半伪补代数，且一元运算f和*由恒等式[f(x)]*=f2(x)与f(x*)=x**所连结。首先刻画了滤子的性质及其同余特征，然后考虑了它们的同余一致与同余凝聚性质。 In first part of the thesis, we study of Ockham algebras with Heytingstructures /(L;∧,∨,→,f,0,1/), where /(L;∧,∨,f,0,1/) is an Ockham algebra,/(L;∧,∨,→,0,1/) is a Heyting-algebra, and the operations x/(?/)f/(x/) and x/(?/)x~*satisfy the identities f/(x→y/) = f~2/(x/) A f/(y/) and f/(x/)→y = f~2/(x/)∨y.We shall denote by HO the class of these algebras. We show that if L is HO-algebra,then ConL/(?/)CKF/(L/), where CKF/(L/) denotes the set of all of thecokernel filters. Furthermore, we show that if L∈HO is *-semi-simple subdirectlyirreducible, there are precisely two non-isomorphic subdirectly irreduciblemembers in the class of these algebras and give a complete description of them. In the second part, we investigate the filters of Ockham algebras with balanceddemi-pseudocomplementation. An Ockham algebra with balanced demipseudocomplementationalgebra /(briefly, bdpO-algebra/) is an algebra /(L;∧,∨,f,*,0,1/)of type <2,2,1,1,0,0>, in which /(L; f/) is an Ockham algebra, /(L,*/) is a demipseudocomplementedalgebra, and the unary operations f and * are linked bythe identities /[f/(x/)/]~* = f~2/(x/) and f/(x~*/) = x~/(**/). we study of properties and givea description of congruence characterizations of filters of bdpO-algebras, andwe also characterize congruence uniformity and congruence coherency on somespecial filters.

关 键 词： 结构 代数 不可约代数 滤子 同余一致

分 类 号： [O153]

领　　域： [理学] [理学]