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1.
Ján Jakubík 《Czechoslovak Mathematical Journal》2009,59(1):183-196
In this paper we deal with a pseudo effect algebra
possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein,
can be represented as an interval of a unital partially ordered group G. We prove that
is projectable (strongly projectable) if and only if G is projectable (strongly projectable). An analogous result concerning weak homogeneity of
and of G is shown to be valid.
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
2.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(3):849-863
In this paper we deal with weakly homogeneous direct factors of lattice ordered groups. The main result concerns the case
when the lattice ordered groups under consideration are archimedean, projectable and conditionally orthogonally complete.
Supported by VEGA grant 2/4134/24.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information. 相似文献
3.
Jan Jakubik 《Czechoslovak Mathematical Journal》2001,51(3):661-671
The distinguished completion E(G) of a lattice ordered group G was investigated by Ball [1], [2], [3]. An analogous notion for MV-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group G is a direct product of lattice ordered groups G
i
(i I), then E(G) is a direct product of the lattice ordered groups E(G
i). From this we obtain a generalization of a result of Ball [3]. 相似文献
4.
Jan Jakubik 《Czechoslovak Mathematical Journal》2001,51(1):127-138
The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4]. 相似文献
5.
Ján Jakubík 《Czechoslovak Mathematical Journal》2008,58(3):717-723
Let Δ and H be a nonzero abelian linearly ordered group or a nonzero abelian lattice ordered group, respectively. In this paper we prove
that the wreath product of Δ and H fails to be affine complete.
Supported by VEGA grant 2/4134/24.
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
6.
Ján Jakubík 《Mathematica Slovaca》2008,58(6):739-754
In this paper we investigate sequential convergences on a cyclically ordered group G which are compatible with the group operation and with the relation of cyclic order; we do not assume the validity of the
Urysohn’s axiom. The system convG of convergences under consideration is partially ordered by means of the set-theoretical inclusion. We prove that convG is a Brouwerian lattice.
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
7.
Jan Jakubik 《Czechoslovak Mathematical Journal》2001,51(4):889-896
In this paper we investigate the possibility of a regular embedding of a lattice ordered group into a completely distributive vector lattice. 相似文献
8.
Ján Jakubík 《Czechoslovak Mathematical Journal》2004,54(2):499-507
Let be an infinite cardinal. In this paper we define an interpolation rule IR() for lattice ordered groups. We denote by C() the class of all lattice ordered groups satisfying IR(), and prove that C() is a radical class. 相似文献
9.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):469-482
In this paper we investigate the relations between torsion classes of Specker lattice ordered groups and torsion classes of generalized Boolean algebras. 相似文献
10.
In the theory of lattice-ordered groups, there are interesting examples of properties — such as projectability — that are defined in terms of the overall structure of the lattice-ordered group, but are entirely determined by the underlying lattice structure. In this paper, we explore the extent to which projectability is a lattice-theoretic property for more general classes of algebras of logic. For a class of integral residuated lattices that includes Heyting algebras and semi-linear residuated lattices, we prove that a member of such is projectable iff the order dual of each subinterval [a,1] is a Stone lattice. We also show that an integral GMV algebra is projectable iff it can be endowed with a positive Gödel implication. In particular, a ΨMV or an MV algebra is projectable iff it can be endowed with a Gödel implication. Moreover, those projectable involutive residuated lattices that admit a Gödel implication are investigated as a variety in the expanded signature. We establish that this variety is generated by its totally ordered members and is a discriminator variety. 相似文献
11.
12.
Jan Jakubik 《Czechoslovak Mathematical Journal》2005,55(4):917-922
In this paper it is proved that an abelian lattice ordered group which can be expressed as a nontrivial lexicographic product
is never affine complete.
This work was supported by VEGA grant 2/1131/21. 相似文献
13.
On the Affine Completeness of Lattice Ordered Groups 总被引:2,自引:2,他引:0
Ján Jakubík 《Czechoslovak Mathematical Journal》2004,54(2):423-429
In the paper it is proved that a nontrivial direct product of lattice ordered groups is never affine complete. 相似文献
14.
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
15.
16.
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
17.
Ján Jakubík 《Mathematica Slovaca》2008,58(5):521-534
A class of lattice ordered groups is called a formation if it is closed with respect to homomorphic images and finite subdirect
products. Analogously we define the formation of GMV-algebras. Let us denote by ℱ1 and ℱ2 the collection of all formations of lattice ordered groups or of GMV-algebras, respectively. Both ℱ1 and ℱ2 are partially ordered by the class-theoretical inclusion. We prove that ℱ1 satisfies the infinite distributivity law
and that ℱ2 is isomorphic to a principal ideal of ℱ1.
This work was supported by VEGA grant 2/7141/27. 相似文献
18.
设S是有向序半群,本文给出了S上的一类正则同余,称为强序同余的定义及性质.证明了S的强序同余是强正则同余,但反之不成立.同时证明了强序同余格SOC(S)是S的同余格C(S)关于通常集合的交和传递积的V-完备的分配子格. 相似文献
19.
Ivica Gusic 《Proceedings of the American Mathematical Society》1998,126(9):2593-2597
We show that a lattice ordered group can be topologized in a natural way. The topology depends on the choice of a set of admissible elements (-topology). If a lattice ordered group is 2-divisible and satisfies a version of Archimedes' axiom (-group), then we show that the -topology is Hausdorff. Moreover, we show that a -group with the -topology is a topological group.
20.
W. J. Blok C. J. van Alten 《Transactions of the American Mathematical Society》2005,357(10):4141-4157
The finite embeddability property (FEP) for integral, commutative residuated ordered monoids was established by W. J. Blok and C. J. van Alten in 2002. Using Higman's finite basis theorem for divisibility orders we prove that the assumptions of commutativity and associativity are not required: the classes of integral residuated ordered monoids and integral residuated ordered groupoids have the FEP as well. The same holds for their respective subclasses of (bounded) (semi-)lattice ordered structures. The assumption of integrality cannot be dropped in general--the class of commutative, residuated, lattice ordered monoids does not have the FEP--but the class of -potent commutative residuated lattice ordered monoids does have the FEP, for any .