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Weak alg-universality and Q -universality of semigroup quasivarieties

Marie Demlová, Václav Koubek (2005)

Commentationes Mathematicae Universitatis Carolinae

In an earlier paper, the authors showed that standard semigroups 𝐌 1 , 𝐌 2 and 𝐌 3 play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by 𝐌 2 and 𝐌 3 are neither relatively alg-universal nor Q -universal, while there do exist finite semigroups 𝐒 2 and 𝐒 3 generating the same semigroup variety as 𝐌 2 and 𝐌 3 respectively and the quasivarieties generated by 𝐒 2 and/or 𝐒 3 are quasivar-relatively f f -alg-universal and Q -universal...

Weak Baer modules over graded rings

Mark Teply, Blas Torrecillas (1998)

Colloquium Mathematicae

In [2], Fuchs and Viljoen introduced and classified the B * -modules for a valuation ring R: an R-module M is a B * -module if E x t R 1 ( M , X ) = 0 for each divisible module X and each torsion module X with bounded order. The concept of a B * -module was extended to the setting of a torsion theory over an associative ring in [14]. In the present paper, we use categorical methods to investigate the B * -modules for a group graded ring. Our most complete result (Theorem 4.10) characterizes B * -modules for a strongly graded ring R...

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