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
收藏
页码：190 / 206
页数：17
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