zbMATH — the first resource for mathematics

Injective objects in categories of monoid representations. (English. Russian original) Zbl 0572.08002
Math. Notes 36, 570-577 (1984); translation from Mat. Zametki 36, No. 2, 159-170 (1984).
Let \(\Gamma\) be an abelian quasivariety in the sense of A. G. Kurosh [General Algebra (Russian; 1974; Zbl 0289.00004)]. If \(\Gamma\) has enough injective objects, then so does, for each monoid R, the category of all representations of R in \(\Gamma\).
Reviewer: J.Adámek
08A60 Unary algebras
08B30 Injectives, projectives
08C15 Quasivarieties
PDF BibTeX Cite
Full Text: DOI
[1] A. G. Kurosh, General Algebra [in Russian], Nauka, Moscow (1974).
[2] L. A. Skornyakov, ?A general view on monoid representations,? Algebra Logika,20, No. 5, 571-574 (1981).
[3] A. I. Mal’tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).
[4] P. Berthiaume, ?The injective envelope of S-sets,? Can. Math. Bull.,10, No. 2, 261-273 (1967). · Zbl 0149.26103
[5] G. Georgescu, ?Anvelope injective in categoria monoizilor comutativi regula?i,? ?tud. Cerc. Mat.,23, No. 7, 1049-1055 (1971). · Zbl 0248.18014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.