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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
MSC:
08A60 Unary algebras
08B30 Injectives, projectives
08C15 Quasivarieties
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References:
[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
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