On varieties of basic algebras

被引：3

作者：

Chajda, Ivan ^{[1
]}

Halas, Radomir ^{[1
]}

机构：

[1] Palacky Univ, Dept Algebra & Geometry, Fac Sci, Olomouc 77146, Czech Republic

来源：

SOFT COMPUTING | 2015年 / 19卷 / 02期

关键词：

Basic algebra; Commutative basic algebra; Symmetric basic algebra; Defining identity; MV-algebra; Orthomodular lattice;

D O I：

10.1007/s00500-014-1365-y

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

It is known that the variety of commutative basic algebras, the variety of MV-algebras, the variety of orthomodular lattices and hence also the variety of Boolean algebras are proper subvarieties of the variety of basic algebras. In the paper several possible axiomatizations of the variety of basic algebras are provided. The variety of symmetric basic algebras is introduced and shown to be a proper subvariety of the variety of commutative basic algebras, and whose members have the underlying lattices distributive. It is proved that commutative basic algebras can be described as residuated -groupoids.

引用

页码：261 / 267

页数：7

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