共查询到20条相似文献,搜索用时 15 毫秒
1.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(1):161-171
In this paper we investigate the relations between isometries and direct product decompositions of generalized MV-algebras. 相似文献
2.
Ján Jakubík 《Czechoslovak Mathematical Journal》2006,56(4):1215-1227
In this paper we prove a theorem on weak homogeneity of MV-algebras which generalizes a known result on weak homogeneity of Boolean algebras. Further, we consider a homogeneity condition
for MV-algebras which is defined by means of an increasing cardinal property. 相似文献
3.
Ján Jakubík 《Czechoslovak Mathematical Journal》2006,56(1):79-98
In this paper we deal with a homogeneity condition for an MV-algebra concerning a generalized cardinal property. As an application, we consider the homogeneity with respect to α-completeness,
where α runs over the class of all infinite cardinals.
This work was supported by VEGA grant 1/9056/02. 相似文献
4.
Ján Jakubík 《Czechoslovak Mathematical Journal》2003,53(3):641-653
In this paper we deal with the (, )-distributivity of an MV-algebra
, where and are nonzero cardinals. It is proved that if
is singular and (, 2)-distributive, then it is (, )-distributive. We show that if
is complete then it can be represented as a direct product of MV-algebras which are homogeneous with respect to higher degrees of distributivity. 相似文献
5.
Jan Kühr 《Czechoslovak Mathematical Journal》2008,58(2):395-415
We deal with unbounded dually residuated lattices that generalize pseudo MV-algebras in such a way that every principal order-ideal is a pseudo MV-algebra. We describe the connections of these generalized pseudo MV-algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo MV-algebra A by means of the positive cone of a suitable ℓ-group G
A
. We prove that the lattice of all (normal) ideals of A and the lattice of all (normal) convex ℓ-subgroups of G
A
are isomorphic. We also introduce the concept of Archimedeanness and show that every Archimedean generalized pseudo MV-algebra is commutative.
Supported by the Research and Development Council of the Czech Govenrment via the project MSM6198959214. 相似文献
6.
Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single
individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic
GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed.
The first author was supported by the Council of Czech Government, MSM 6198959214. 相似文献
7.
Ján Jakubík 《Czechoslovak Mathematical Journal》2008,58(1):183-202
In the present paper we deal with generalized MV-algebras (GMV-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, GMV-algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract
mappings of GMV-algebras. The relations between GMV-algebras and lattice ordered groups are essential for this investigation.
Supported by VEGA Agency grant 1/2002/05.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information,
grant I/2/2005. 相似文献
8.
Bounded commutative residuated ℓ-monoids are a generalization of algebras of propositional logics such as BL-algebras, i.e. algebraic counterparts of the basic fuzzy logic (and hence consequently MV-algebras, i.e. algebras of the Łukasiewicz infinite valued logic) and Heyting algebras, i.e. algebras of the intuitionistic
logic. Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single
individual variable occurs. We introduce and study monadic residuated ℓ-monoids as a generalization of monadic MV-algebras.
Jiří Rachůnek was supported by the Council of Czech Goverment MSM 6198959214. 相似文献
9.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(1):243-252
The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of
a group is subdirectly irreducible. For an MV-algebra
we denote by
, A and
the idempotent modification, the underlying set or the underlying lattice of
, respectively. In the present paper we prove that if
is semisimple and
is a chain, then
is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras. 相似文献
10.
Ján Jakubík 《Mathematica Slovaca》2008,58(2):143-154
For an MV-algebra
let J
0(
) be the system of all closed ideals of
; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV-algebras will be called a K-radical class iff, whenever
∈ X and
is an MV-algebra with J
0(
) ≅ J
0(
), then
∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that
there is a one-to-one correspondence between K-radical classes of MV-algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV-algebras; product radical classes of lattice ordered groups were studied by Ton.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information,
Grant I/2/2005. 相似文献
11.
J. Jakubík 《Czechoslovak Mathematical Journal》2003,53(2):311-317
In the present paper we show that free MV-algebras can be constructed by applying free abelian lattice ordered groups. 相似文献
12.
Ján Jakubík 《Mathematica Slovaca》2008,58(6):719-738
We use the concept of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis; the main tool in their investigation was a truncation construction.
The relations between radical classes of GMV-algebras and radical classes of lattice ordered groups are investigated in the present paper. Further, we apply the truncation
construction for dealing with weak retract mappings of GMV-algebras.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of
Information (Grant I/2/2005). 相似文献
13.
In analogy with effect algebras, we introduce the test spaces and MV-test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between MV-algebras and MV-test spaces. 相似文献
14.
The class of commutative dually residuated lattice ordered monoids (DRℓ-monoids) contains among others Abelian lattice ordered groups, algebras of Hájek’s Basic fuzzy logic and Brouwerian algebras.
In the paper, a unary operation of negation in bounded DRℓ-monoids is introduced, its properties are studied and the sets of regular and dense elements of DRℓ-monoids are described. 相似文献
15.
Complete Subobjects of Fuzzy Sets Over MV-Algebras 总被引:1,自引:1,他引:1
Jiří Močkoř 《Czechoslovak Mathematical Journal》2004,54(2):379-392
A subobjects structure of the category -FSet of -fuzzy sets over a complete MV-algebra
is investigated, where an -fuzzy set is a pair A = (A, ) such that A is a set and : A × A is a special map. Special subobjects (called complete) of an -fuzzy set A which can be identified with some characteristic morphisms
A * = (L × L, ) are then investigated. It is proved that some truth-valued morphisms
are characteristic morphisms of complete subobjects. 相似文献
16.
Bounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure
operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROVá,M.—RACHŮNEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras.
The first author was supported by the Council of Czech Government, MSM 6198959214. 相似文献
17.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):651-663
Let Int
be the lattice of all intervals of an MV-algebra
. In the present paper we investigate the relations between direct product decompositions of
and (i) the lattice Int
, or (ii) 2-periodic isometries on
, respectively. 相似文献
18.
M. V. Balashov 《Mathematical Notes》2002,71(3-4):295-304
19.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(4):1099-1105
A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element.
This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002.
The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information
(grant I/2/2005). 相似文献
20.
Anatolij Dvurečenskij 《Czechoslovak Mathematical Journal》2006,56(1):47-59
We give two variations of the Holland representation theorem for ℓ-groups and of its generalization of Glass for directed
interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that
every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo MV-algebra can be represented as a pseudo-effect algebra or as a pseudo MV-algebra of automorphisms of some antilattice or of some linearly ordered set. 相似文献