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 .

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Simultaneously reflective and coreflective subcategories of presheaves.

On functors which are lax epimorphisms.

A new proof of Prüfer's theorem

Modules commuting (via Hom) with some limits

Commutative zeropotent semigroups with few invariant congruences

Notes on slender prime rings

Quasitrivial left distributive groupoids

Modules commuting (via Hom) with some colimits

Commutative semigroups with few fully invariant congruences I.

Dually steady rings

Commutative semigroups with few fully invariant congruences II.

Simple zeropotent paramedial groupoids are balanced