Displaying similar documents to “Remarks on C-independence in Cartesian products of abstract algebras”

On Singer's algebra and coalgebra structures

Luciano A. Lomonaco (2006)

Bollettino dell'Unione Matematica Italiana

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Recently W. M. Singer has introduced the notion of algebra with coproducts (and the dual notion of coalgebra with products) by somehow weakening the notion of Hopf algebra (see [6]). In this paper we consider certain algebras of invariants and show that they are, in fact, further examples of algebras with coproducts and coalgebras with products. Moreover, we discuss the close relation between such algebras and the structures considered in Singer's paper.

The class of 2-dimensional neat reducts is not elementary

Tarek Sayed Ahmed (2002)

Fundamenta Mathematicae

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SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends...