伪对合剩余格(非可换)与伪效应代数(英文)

Pseudo-involutive Residuated Lattices(Non-commutative) and Pseudo-effect Algebras

提出伪对合剩余格(非可换)的概念。通过在伪效应代数中引入两个部分运算,研究了伪对合剩余格与格伪效应代数之间的自然关系,证明了以下结论:在一定条件下,一个格伪效应代数可被扩张成为一个伪对合剩余格,同时一个伪对合剩余格可被限制为一个格伪效应代数。特别地,得到伪对合剩余格成为具有Riesz分解性质的格伪效应代数的一个充要条件。最后,还讨论了伪效应代数与剩余格的理想与滤子理论。

The notion of pseudo-involutive residuated lattices （non-commutative） is introduced. By introducing two partial operations in pseudo-effeet algebras, the mutual relationship between pseudo-involutive residuated lattices and lattice pseudo-effect algebras are investigated. The following results are proved： a lattice pseudo- effect algebra under certain conditions ean be extended to a pseudo-involutive residuated lattice and the latter with certain properties can be restricted to the former. Especially, a sufficient and necessary condition for a pseudo-involutive residuated lattice to be lattice pseudo-effect algebra with the Riesz decomposition property is obtained. Finally,the ideals and filters of pseudo-effect algebras and pseudo residuated lattices are investigated.