منابع مشابه
Totally Ordered Commutative Semigroups
Let 5( + , < ) be a system consisting of a set S endowed with an associative binary operation + and a total ( = linear = simple) order relation < . The composition + and the relation < may be connected by either or both of the following conditions. MC (Monotone Condition). If a and b are elements of 5 such that ax+y ...
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In this paper, we describe all equational theories of commutative semigroups in terms of certain well-quasi-orderings on the set of finite sequences of nonnegative integers. This description yields many old and new results on varieties of commutative semigroups. In particular, we obtain also a description of the lattice of varieties of commutative semigroups, and we give an explicit uniform sol...
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In this paper; we study equations on semidirect products of commutative semigroups. Let Comq,r denote the pseudovariety of all finite semigroups that satisfy the equations xy = yx and x r + q = xr. The pseudovariety Com1,1 is the pseudovariety of all finite semilattices. We consider the product pseudovariety Comq,r * generated by all semidirect products of the form S*T with S ∈ Comq,r and T ∈ ,...
متن کاملCommutative cancellative semigroups of finite rank
The rank of a commutative cancellative semigroup S is the cardinality of a maximal independent subset of S. Commutative cancellative semigroups of finite rank are subarchimedean and thus admit a Tamura-like representation. We characterize these semigroups in several ways and provide structure theorems in terms of a construction akin to the one devised by T. Tamura for N-semigroups.
متن کاملBases for commutative semigroups and groups
A base for a commutative semigroup (S,+) is an indexed set 〈xt〉t∈A in S such that each element x ∈ S is uniquely representable as ∑t∈F xt where F is a finite subset of A and, if S has an identity 0, then 0 = ∑n∈ xt . We investigate those commutative semigroups or groups which have a base. We obtain the surprising result that Q has a base. More generally, we show that an abelian group has a base...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1991
ISSN: 0263-6115
DOI: 10.1017/s144678870003456x