منابع مشابه
Boolean Powers of Groups
A group is ^-separating if a Boolean power of the group has a unique Boolean algebra. It is proved that a finite subdirectly irreducible group is S-separating if and only if it is non-Abelian. Suppose B is a Boolean ring and G is a group. Let B[G] denote the group ring of G with coefficient ring B. The Boolean power G [B] is defined to be the set of those elements 2e,.g,. EB[G] such that (1) 2e...
متن کاملBoolean Powers of Abelian Groups
where (f + g)(u) = V_,,+,,,f(v) A f(w). Since E is countable, ZcB) can be defined for any countably complete Boolean algebra (ccBa) B where Z is the group of the integers. This kind of group was first (1962) studied by Balcerzyk [l]. However, it seems that not much attention was paid to such groups for a rather long period. Under the point of view in [l, Theorem 51 and [13, Proposition 11, it c...
متن کاملOn the Sequence of Consecutive Matrix Powers of Boolean Matricesin
In this paper we consider sequences of consecutive powers of boolean matrices in the max-plus algebra, which is one of the frameworks that can be used to model certain classes of discrete event systems. The ultimate behavior of a sequence of consecutive max-plus-algebraic powers of a boolean matrix is cyclic. First we derive upper bounds for the length of the cycles as a function of the size of...
متن کاملIdempotent generated algebras and Boolean powers of commutative rings
Boolean powers were introduced by Foster [5]. It was noticed by Jónsson in the review of [6], and further elaborated by Banaschewski and Nelson [1], that the Boolean power of an algebra A by a Boolean algebra B can be described as the algebra of continuous functions from the Stone space of B to A, where A has the discrete topology. It follows that a Boolean power of the group Z is an `-group ge...
متن کاملOmega-almost Boolean rings
In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1969
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-65-3-243-268