Probabilistic averaging in bounded Rl-monoids

被引：66

作者：

Dvurecenskij, A

Rachunek, J

机构：

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

[2] Palacky Univ, Fac Sci, Dept Algebra & Geometry, CZ-77900 Olomouc, Czech Republic

来源：

SEMIGROUP FORUM | 2006年 / 72卷 / 02期

关键词：

bounded Rl-monoid; state (= Bosbach state); state-morphism; filter; normal filter; maximal filter; pseudo MV-algebra (= GMV-algebra); pseudo BL-algebra;

D O I：

10.1007/s00233-005-0545-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Bounded Rl-monoids generalize GMV-algebras and pseudo BL-algebras. Such monoids do not admit, in general, any analogue of addition, in contrast to GMV-algebras. Nevertheless we introduce the notion of a state (an analogue of a probability measure). It coincides with that for GMV-algebras. We show that the existence of states is crucially connected with the existence of normal and maximal filters. In addition, some topological properties of the extremal states and the hull-kernel topology of filters are studied.

引用

页码：190 / 206

页数：17

共 26 条

[1] [Anonymous], 1986, MATH SURVEYS MONOGR
[2] Cancellative residuated lattices
Bahls, P
Cole, J
Galatos, N
Jipsen, P
Tsinakis, C
[J]. ALGEBRA UNIVERSALIS, 2003, 50 (01) : 83 - 106
[3] The structure of residuated lattices
Blount, K
Tsinakis, C
[J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2003, 13 (04) : 437 - 461
[4] Bosbach B., 1982, RESULTATE MATH, V5, P107
[5] Chang C. C., 1958, Trans. Amer. Math. Soc., V88, P467, DOI DOI 10.1090/S0002-9947-1958-0094302-9
[6] Cignoli R. L, 2013, Algebraic foundations of many-valued reasoning, V7
[7] Di Nola A., 2002, Multiple-Value Logic, V8, P717
[8] Non-commutative residuated lattices
Dilworth, R. P.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1939, 46 (1-3) : 426 - 444
[9] DINOLA A, 2002, MULTIPLE VALUED LOGI, V8, P673
[10] Pseudo MV-algebras are intervals in l-groups
Dvurecenskij, A
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2002, 72 : 427 - 445

← 1 2 3 →