两类P-代数的刻划

CHARACTERIZATIONS OF TWO CLASSES OF p-ALGEBRAS

我们称满足条件x~*Vx^(**)=1的P—代数为S—代数,满足条件x=x^(**)A(x~*Vx^(**))的p-代数为强可分解p代数。本文的主要结果为:(1)一个p-代数L是S代数的充要条件是它不包含任何H作为子代数。(2)一个p-代数L是强可分解p-代数的充要条件是它不包含任何K_1、K_2、K_3和K_4作为子代数。

A p-algebra or a pseudocomplemented algebra is a universal algebra ( L; V. 0, 1 ) of type ( 2, 2, 1. 0, 0 ) , where ( L; V, . 0, 1 ) is a bounded lattice and, for every aeL, the element a is a pseudocomplement of a, i. e. x<a if x Aa = 0. A p-algebra is called an S-algebra if x Vx=1 for any xeL. A p-algebra L called strongly decomposable p-algebra if x = xA (xVx) for any xeL. The main results of this note read as follows Theorem 1 A p-algebra L is an S-algebra if and only if it does not contain any H as its subalgbra. Theorem 2 A p-algebra L is a strongly decomposable p-algebra if and only if it does not contain any of K1 K2 K3 or K4 as its subalgebras