A Representation of Lattice Effect Algebras by Means of Right Near Semirings with Involution

被引：7
|
作者：
Chajda, Ivan [1 ]
Laenger, Helmut [2 ]
机构：
[1] Palacky Univ, Fac Sci, Dept Algebra & Geometry, 17 Listopadu 12, Olomouc 77146, Czech Republic
[2] TU Wien, Inst Discrete Math & Geometry, Fac Math & Geoinformat, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
来源：
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 2017年 / 56卷 / 12期
基金：
奥地利科学基金会;
关键词：
Effect algebra; Lattice effect algebra; Right near semiring; Antitone involution; Effect near semiring;
D O I：
10.1007/s10773-016-3191-8
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Since every lattice effect algebra decomposes into blocks which are MV-algebras and since every MV-algebra can be represented by a certain semiring with an antitone involution as shown by Belluce, Di Nola and Ferraioli, the natural question arises if a lattice effect algebra can also be represented by means of a semiring-like structure. This question is answered in the present paper by establishing a one-to-one correspondence between lattice effect algebras and certain right near semirings with an antitone involution.
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页码：3719 / 3726
页数：8
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