H-PERFECT PSEUDO MV-ALGEBRAS AND THEIR REPRESENTATIONS

被引：4

作者：

Dvurecenskij, Anatolij ^{[1
,2
]}

机构：

[1] Slovak Acad Sci, Math Inst, SK-81473 Bratislava, Slovakia

[2] Palacky Univ, Dept Algebra & Geometry, CZ-77146 Olomouc, Czech Republic

来源：

MATHEMATICA SLOVACA | 2015年 / 65卷 / 04期

关键词：

pseudo MV-algebra; l-group; unital l-group; strong unit; Riesz Decomposition Property; lexicographic product; H-perfect pseudo MV-algebra; strong H-perfect pseudo MV-algebra; weak H-perfect pseudo MV-algebra; GMV-ALGEBRAS; VARIETIES;

D O I：

10.1515/ms-2015-0054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study H-perfect pseudo MV-algebras, that is, algebras which can be split into a system of ordered slices indexed by the elements of an subgroup H of the group of the real numbers. We show when they can be represented as a lexicographic product of H with some l-group. In addition, we show also a categorical equivalence of this category with the category of l-groups.

引用

页码：761 / 788

页数：28

共 50 条

[1] Pseudo MV-algebras and lexicographic product
Dvurecenskij, Anatolij
FUZZY SETS AND SYSTEMS, 2016, 303 : 56 - 79
[2] Lexicographic pseudo MV-algebras
Dvurecenskij, Anatolij
JOURNAL OF APPLIED LOGIC, 2015, 13 (04) : 825 - 841
[3] Orthocomplete pseudo MV-algebras
Dvurecenskij, A.
Zahiri, O.
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 2016, 45 (7-8) : 889 - 909
[4] Bricks and pseudo MV-algebras are equivalent
Subrahmanyam, N. V.
MATHEMATICA SLOVACA, 2008, 58 (02) : 131 - 142
[5] On a generalization of pseudo MV-algebras
Kuhr, Jan
JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING, 2006, 12 (5-6) : 373 - 389
[6] ON HYPER PSEUDO MV-ALGEBRAS
Borzooei, R. A.
Zahiri, O.
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2014, (33): : 201 - 224
[7] Pseudo MV-algebras are intervals in l-groups
Dvurecenskij, A
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2002, 72 : 427 - 445
[8] Generalizations of pseudo MV-algebras and generalized pseudo effect algebras
Kuhr, Jan
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2008, 58 (02) : 395 - 415
[9] Some results on pseudo MV-algebras with square roots
Dvurecenskij, Anatolij
Zahiri, Omid
FUZZY SETS AND SYSTEMS, 2023, 465
[10] Good and bad infinitesimals, and states on pseudo MV-algebras
Di Nola, A
Dvurecenskij, A
Jakubík, J
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2004, 21 (04): : 293 - 314

← 1 2 3 4 5 →