共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
We consider the varieties of lattice ordered groups with the identity of commutation of the nth powers of elements. We establish that every such l-variety with n=pq, where p and q are distinct prime numbers, has a finite basis of identities. 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.
Martha L. H. Kilpack 《代数通讯》2018,46(4):1387-1396
We say a lattice L is a subgroup lattice if there exists a group G such that Sub(G)?L, where Sub(G) is the lattice of subgroups of G, ordered by inclusion. We prove that the lattice of closure operators which act on the subgroup lattice of a finite group G is itself a subgroup lattice if and only if G is cyclic of prime power order. 相似文献
5.
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
6.
G. Grä tzer E. T. Schmidt 《Proceedings of the American Mathematical Society》1999,127(7):1903-1915
In 1962, the authors proved that every finite distributive lattice can be represented as the congruence lattice of a finite sectionally complemented lattice. In 1992, M. Tischendorf verified that every finite lattice has a congruence-preserving extension to an atomistic lattice. In this paper, we bring these two results together. We prove that every finite lattice has a congruence-preserving extension to a finite sectionally complemented lattice.
7.
8.
Weakly associative lattice rings (wal-rings) are non-transitive generalizations of lattice ordered rings (l-rings). As is known, the class of l-rings which are subdirect products of linearly ordered rings (i.e. the class of f-rings) plays an important role in the theory of l-rings. In the paper, the classes of wal-rings representable as subdirect products of to-rings and ao-rings (both being non-transitive generalizations of the class of f-rings) are characterized and the class of wal-rings having lattice ordered positive cones is described. Moreover, lexicographic products of weakly associative lattice groups are also studied here. 相似文献
9.
Jan Jakubik 《Czechoslovak Mathematical Journal》2005,55(4):957-973
In this paper we prove that the lateral completion of a projectable lattice ordered group is strongly projectable. Further,
we deal with some properties of Specker lattice ordered groups which are related to lateral completeness and strong projectability.
This work was supported by VEGA grant 2/1131/21. 相似文献
10.
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
11.
§1. IntroductionIn1995,Mr.XuYang,inhisdoctoraldissertation[1],firstintroducedadoublelattice-or-deredalgebraicstructurecalledl-moduleanddiscusseditsalgebraicandanalyticalproperties,bywhichhedealtwiththeproblemoflattice-valuedgameandsetuptheelementalt… 相似文献
12.
Marta Vrábelová 《Czechoslovak Mathematical Journal》2007,57(1):95-103
A lattice ordered group valued subadditive measure is extended from an algebra of subsets of a set to a σ-algebra. 相似文献
13.
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 .
14.
Sub(L)中的五边形格特征及其数量不等式 总被引:1,自引:0,他引:1
五边形结构在刻画格的特征方面具有十分重要作用,应用格论及组合数学的方法讨论了格L与其子格格Sub(L)中所含五边形格之间的数量关系,给出了有限格L的子格格中三个元生成五边形格的充要条件,同时给出了Sub(L)所含不同五边形格数量的一个下界。 相似文献
15.
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
16.
Let Co(V) be a lattice of convex subsets of a vector space V over a totally ordered division ring
. We state that every lattice L can be embedded into Co(V), for some space V over
. Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional; in this case L also embeds into a finite lower bounded lattice of the form Co(V,)={X | X Co(V)}, for some finite subset of V. This result yields, in particular, a new universal class of finite lower bounded lattices. 相似文献
17.
Jan Kühr 《Czechoslovak Mathematical Journal》2005,55(1):97-111
In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence. 相似文献
18.
19.
Curtis Bennett Kathy J. Dempsey Bruce E. Sagan 《Journal of Algebraic Combinatorics》1994,3(3):261-283
We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F
q. Another member is constructed so as to mirror the partial order in the subspace lattice. 相似文献
20.
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