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1
Content available remote Minimal growth function of uniform amenability for discrete abelian groups
Witowicz P.
Bulletin of the Polish Academy of Sciences. Mathematics
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2018
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Vol. 66, no. 2
135--141
EN
We give new properties of the minimal growth function for uniformly amenable abelian groups in which orders of elements are not uniformly bounded.
2
Liczby niepewne
Borawski M.
Metody Informatyki Stosowanej
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2007
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nr 2(Tom 12)
27-34
EN
In the article, the origin of number systems, which describe the uncertain information is handled. Two different possibilities of creating such systems are shown. The convolution representation and its connection with fuzzy arithmetic and algebra is introduced. On this basis the need of defining a new conception of the certain number is proved. The new conception of such, numbers is defined in the article.
3
Content available remote Compression bases in effect algebras
Gudder S.
Demonstratio Mathematica
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2006
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Vol. 39, nr 1
43-54
EN
We generalize David Foulis's concept of a compression base on a unital group to effect algebras. We first show that the compressions of a compressible effect algebra form a compression basis and that a sequential effect algebra possesses a natural maximal compression basis. It is then shown that many of the results concerning compressible effect algebras hold for arbitrary effect algebras by focusing on a specific compression base. For example, the foci (or projections) of a compression base form an orthomodular poset. Moreover, one can give a natural definition for the commutant of a projection in a compression base and results concerning order and compatibility of projections can be generalized. Finally it is shown that if a compression base has the projection-cover property, then the projections of the base form an orthomodular lattice
4
Content available remote Comparability groups
Foulis D., Foulis D.
Demonstratio Mathematica
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2006
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Vol. 39, nr 1
15-32
EN
A comparability group is a unital group with a compression base and with the general comparability property. The additive group of self-adjoint elements in a von Neumann algebra, and any Dedekind sigma-complete lattice-ordered abelian group with order unit are examples of comparability groups. We develop the basic theory of comparability groups, and show that an archimedean comparability group with the Rickart projection property can be embedded in a partially ordered rational vector space the elements of which admit a rational spectral resolution.
5
Content available remote On some sets of identities satisfied in Abelian groups
Gajewska-Kurdziel K., Mruczek K.
Demonstratio Mathematica
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2002
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Vol. 35, nr 3
447-453
EN
The equational theories were studied in many works (see [4], [5], [6], [7]). Let T be a type of Abelian groups. In this paper we consider the extentions of the equational theory Ex(Gn) defined by so called externally compatible identities of Abelian groups and the identity xn = yn. The equational base of this theory was found in [3]. We prove that each equational theory Cn(Ex^(Gn) U {(phi=epsilon}), where phi=epsilon is an identity of type r, is equal to the extension of the equational theory Cn{Ex{Gn) U E), where E is a finite set of one variable identities of type r. The notation in this paper are the same as in [1].
6
Content available remote An extension of a result of A. D. Sands
Szabo S.
Demonstratio Mathematica
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2000
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Vol. 33, nr 3
459-465
EN
A. D. Sands showed that if a group of type (22,22) is a direct product of its subsets of order 4, then at least one of these subsets must be periodic. In this paper we prove a result about groups of type (2\,2X) that generalizes Sands' theorem.
7
Content available remote 0-1 law for product measures in product of groups
Wiśniewski A.
Demonstratio Mathematica
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2000
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Vol. 33, nr 4
901-908
EN
The 0-1 law for measurable subgroups and cosets in arbitrary product of Abelian groups with product measure is investigated.
8
Content available remote Homomorphisms of the group L1/2 into L1/2 and L1/3
Chudziak J., Drygaś P., Jabłoński W., Midura S.
Demonstratio Mathematica
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1998
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Vol. 31, nr 1
143-152
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