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Currently displaying 1 – 12 of 12

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A new proof of Prüfer's theorem

Robert El Bashir — 1993

Acta Universitatis Carolinae. Mathematica et Physica

Modules commuting (via Hom) with some limits

Robert El Bashir; Tomáš Kepka — 1998

Fundamenta Mathematicae

For every module M we have a natural monomorphism $Φ : ∐_{i \in I} H o m_{R} (A_{i}, M) \to H o m_{R} (\prod_{i \in I} A_{i}, M)$ and we focus attention on the case when Φ is also an epimorphism. The corresponding modules M depend on thickness of the cardinal number card(I). Some other limits are also considered.

Commutative zeropotent semigroups with few invariant congruences

Robert El Bashir; Tomáš Kepka — 2008

Czechoslovak Mathematical Journal

Commutative semigroups satisfying the equation $2 x + y = 2 x$ and having only two $G$ -invariant congruences for an automorphism group $G$ are considered. Some classes of these semigroups are characterized and some other examples are constructed.

Notes on slender prime rings

Robert El Bashir; Tomáš Kepka — 1996

Commentationes Mathematicae Universitatis Carolinae

If $R$ is a prime ring such that $R$ is not completely reducible and the additive group $R (+)$ is not complete, then $R$ is slender.

Quasitrivial left distributive groupoids

Robert El Bashir; Aleš Drápal — 1994

Commentationes Mathematicae Universitatis Carolinae

Left distributive quasitrivial groupoids are completely described and those of them which are subdirectly irreducible are found. There are also determined all left distributive algebras $A = A (*, \circ)$ such that $A (*)$ is a quasitrivial groupoid.

Modules commuting (via Hom) with some colimits

Robert El Bashir; Tomáš Kepka; Petr Němec — 2003

Czechoslovak Mathematical Journal

For every module $M$ we have a natural monomorphism $Ψ : \underset{i \in I}{∐} {H o m}_{R} (M, A_{i}) \to {H o m}_{R} (M, \underset{i \in I}{∐} A_{i})$ and we focus our attention on the case when $Ψ$ is also an epimorphism. Some other colimits are also considered.

This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .