Ideals and quotients in lattice ordered effect algebras

被引：31

作者：

G. Jenča

S. Pulmannová

机构：

[1] Department of Mathematics,

[2] Faculty of Electrical Engineering and Information Technology,undefined

[3] Slovak University of Technology,undefined

[4] Ilkovičova 3,undefined

[5] 812 19 Bratislava,undefined

[6] Slovakia E-mail: jenca@kmat.elf.stuba.sk,undefined

[7] Mathematical Institute,undefined

[8] Slovak Academy of Sciences,undefined

[9] Stefánikova 49,undefined

[10] 814 73 Bratislava,undefined

[11] Slovakia E-mail: pulmann@mat.savba.sk,undefined

来源：

Soft Computing | 2001年 / 5卷 / 5期

关键词：

Prime Ideal; Effect Algebra; Generalize Commutator; Riesz Ideal; Lattice Order Effect Algebra;

D O I：

10.1007/s005000100139

中图分类号：

学科分类号：

摘要：

We show that a quotient of a lattice ordered effect algebra L with respect to a Riesz ideal I is linearly ordered if and only if I is a prime ideal, and the quotient is an MV-algebra if and only if I is an intersection of prime ideals. A generalization of the commutators in OMLs is defined in the frame of lattice ordered effect algebras, such that the quotient with respect to a Riesz ideal I is an MV-algebra if and only if I contains all generalized commutators. If L is an OML, generalized commutators coincide with the usual Marsden commutators.

引用

页码：376 / 380

页数：4