HIGHER DEGREES OF DISTRIBUTIVITY IN COMPLETE GENERALIZED MV-ALGEBRAS

被引：0

作者：

Jakubik, Jan ^{[1
]}

机构：

[1] Slovak Acad Sci, Math Inst, SK-04001 Kosice, Slovakia

来源：

MATHEMATICA SLOVACA | 2011年 / 61卷 / 03期

关键词：

generalized MV-algebra; completeness; higher degrees of distributivity; direct product; LATTICE-ORDERED GROUPS; MAPPINGS;

D O I：

10.2478/s12175-011-0016-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply the notion of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis. Let M be a complete GMV-algebra and let alpha be a cardinal. We prove that M is alpha-distributive if and only if it is (alpha, 2)-distributive. We deal with direct summands of M which are homogeneous with respect to higher degrees of distributivity. (C) 2011 Mathematical Institute Slovak Academy of Sciences

引用

页码：341 / 354

页数：14

共 19 条

[1] Higher Degrees of Distributivity in MV-Algebras
Ján Jakubík
Czechoslovak Mathematical Journal, 2003, 53 : 641 - 653
[2] Higher degrees of distributivity in MV-algebras
Jakubík, J
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2003, 53 (03) : 641 - 653
[3] Weak (m, n)-distributivity of lattice ordered groups and of generalized MV-algebras
Jakubík, J
SOFT COMPUTING, 2006, 10 (02) : 119 - 124
[4] Isometries of generalized MV-algebras
Jakubik, Jan
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2007, 57 (01) : 161 - 171
[5] On idempotent modifications of generalized MV-algebras
Jakubik, Jan
MATHEMATICA SLOVACA, 2010, 60 (02) : 179 - 188
[6] COVERS OF THE ABELIAN VARIETY OF GENERALIZED MV-ALGEBRAS
Dvurecenskij, Anatolij
Holland, W. Charles
COMMUNICATIONS IN ALGEBRA, 2009, 37 (11) : 3991 - 4011
[7] Banaschewski's theorem for generalized MV-algebras
Jakubik, Jan
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2007, 57 (04) : 1099 - 1105
[8] Direct summands and retract mappings of generalized MV-algebras
Jakubik, Jan
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2008, 58 (01) : 183 - 202
[9] (⊙,∨)-Derivations on MV-algebras
Zhao, Xueting
Gan, Aiping
Yang, Yichuan
SOFT COMPUTING, 2024, 28 (03) : 1833 - 1849
[10] On a homogeneity condition for MV-algebras
Ján Jakubík
Czechoslovak Mathematical Journal, 2006, 56 : 79 - 98

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