State-morphism MV-algebras

被引：52

作者：

Di Nola, Antonio ^{[1
]}

Dvurecenskij, Anatolij ^{[2
]}

机构：

[1] Univ Salerno, Dept Math & Informat, I-84084 Salerno, Italy

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

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2009年 / 161卷 / 02期

关键词：

MV-algebra; State; Extremal state; State-morphism; State MV-algebra; State-morphism MV-algebra; THEOREM;

D O I：

10.1016/j.apal.2009.05.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a stronger variation of state MV-algebras, recently presented by T. Flaminio and F. Montagna, which we call state-morphism MV-algebras. Such structures are MV-algebras with an internal notion, a state-morphism operator. We describe the categorical equivalences of such (state-morphism) state MV-algebras with the category of unital Abelian l-groups with a fixed state operator and present their basic properties. In addition, in contrast to state MV-algebras, we are able to describe all subdirectly irreducible state-morphism MV-algebras. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：161 / 173

页数：13

共 50 条

[1] ON SOME CLASSES OF STATE-MORPHISM MV-ALGEBRAS
Di Nola, Antonio
Dvurecenskij, Anatolij
[J]. MATHEMATICA SLOVACA, 2009, 59 (05) : 517 - 534
[2] State-morphism MV-algebras (vol 161, pg 161, 2009)
Di Nola, A.
Dvuretenskij, A.
Lettieri, A.
[J]. ANNALS OF PURE AND APPLIED LOGIC, 2010, 161 (12) : 1605 - 1607
[3] State morphism MV-algebras
Dvurecenskij, Anatolij
Kowalski, Tomasz
Montagna, Franco
[J]. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2011, 52 (08) : 1215 - 1228
[4] State-morphism pseudo-effect algebras
Pulmannova, S.
Vincekova, E.
[J]. SOFT COMPUTING, 2014, 18 (01) : 5 - 13
[5] State-morphism pseudo-effect algebras
S. Pulmannová
E. Vinceková
[J]. Soft Computing, 2014, 18 : 5 - 13
[6] State-morphism algebras-General approach
Botur, Michal
Dvurecenskij, Anatolij
[J]. FUZZY SETS AND SYSTEMS, 2013, 218 : 90 - 102
[7] State BCK-algebras and state-morphism BCK-algebras
Borzooei, R. A.
Dvurecenskij, A.
Zahiri, O.
[J]. FUZZY SETS AND SYSTEMS, 2014, 244 : 86 - 105
[8] Subdirectly irreducible state-morphism BL-algebras
Dvurecenskij, Anatolij
[J]. ARCHIVE FOR MATHEMATICAL LOGIC, 2011, 50 (1-2) : 145 - 160
[9] Subdirectly irreducible state-morphism BL-algebras
Anatolij Dvurečenskij
[J]. Archive for Mathematical Logic, 2011, 50 : 145 - 160
[10] On state monadic MV-algebras
He, Pengfei
Wei, Ya
Wang, Juntao
[J]. FUZZY SETS AND SYSTEMS, 2024, 485

← 1 2 3 4 5 →