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1.
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
2.
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
3.
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
4.
Jan Jakubik 《Czechoslovak Mathematical Journal》2001,51(3):609-616
Riecan [12] and Chovanec [1] investigated states in MV-algebras. Earlier, Riecan [11] had dealt with analogous ideas in D-posets. In the monograph of Riecan and Neubrunn [13] (Chapter 9) the notion of state is applied in the theory of probability on MV-algebras. We remark that a different definition of a state in an MV-algebra has been applied by Mundici [9], [10] (namely, the condition (iii) from Definition 1.1 above was not included in his definition of a state; in other words, only finite additivity was assumed). Below we work with the definition from [13]; but, in order to avoid terminological problems we use the term "state-homomorphism" (instead of "state"). The author is indebted to the referee for his suggestion concerning terminology. Let
be an MV-algebra which is defined on a set A with card A>1. In the present paper we show that there exists a one-to-one correspondence between the system of all state-homomorphisms on
and the system of all -closed maximal ideals of
. For MV-algebras we apply the notation and the definitions as in Gluschankof [3]. The relations between MV-algebras and abelian lattice ordered groups (cf. Mundici [8]) are substantially used in the present paper. 相似文献
5.
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
6.
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
7.
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
8.
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
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.
A DC-space (or space of dense constancies) is a Tychonoff space X such that for each f C(X) there is a family of open sets {U
i
: i I}, the union of which is dense in X, such that f, restricted to each U
i
, is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean f-algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property. 相似文献
11.
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
12.
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
13.
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
14.
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
15.
Denote by Υ1 the collection of quasivarieties of pseudo-MV-algebras; and by Υ2, the collection of quasivarieties of lattice-ordered groups. With respect to the set-theoretic inclusion, Υ1 and Υ2 are lattices. We note some properties of Υ1 and construct an injective mapping φ of Υ2 into Υ1 such that Z 1?Z 2??(Z 1)??(Z 2) for all Z 1, Z 2 ∈ Υ2. 相似文献
16.
Ralf Kemper 《Applied Categorical Structures》2000,8(4):579-593
We show that the results about the set S : ={ [0, 1] 1 / p
x + (1 – )1 / p
z 1 / p
y + (1 – )1 / p
z}, where x, y, z elements of a p-absolutely convex space D and `' is a congruence relation on D are the best possible. Finally, we give an explicit construction of the left adjoint of the comparison functor Ô
p
: B an
p
T C
p
(resp. Ô
p, fin : V ec
p
A C
p
). 相似文献
17.
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
18.
We study a W-algebra of central charge 2(k−1)/(k+2), k=2,3,…, contained in the commutant of a Heisenberg algebra in a simple affine vertex operator algebra L(k,0) of type with level k. We calculate the operator product expansions of the W-algebra. We also calculate some singular vectors in the case k6 and determine the irreducible modules and Zhu's algebra. Furthermore, the rationality and the C2-cofiniteness are verified for such k. 相似文献
19.
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
20.
Ján Jakubík 《Czechoslovak Mathematical Journal》2003,53(1):113-125
For a pseudo MV-algebra
we denote by
the underlying lattice of
. In the present paper we investigate the algebraic properties of maximal convex chains in
containing the element 0. We generalize a result of Dvureenskij and Pulmannová. 相似文献