Geodesic
Completeness and stability of the class of injective
Algebra i logika, Tome 59 (2020) no. 1, pp. 48-65.

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We deal with questions concerning the completeness and stability of a class of injective acts and a class of weakly injective acts over a monoid $S$. The concepts of an injective $S$-act and of a weakly injective $S$-act are analogs of the concept of an injective module. In the theory of modules, the corresponding notions of injectivities in accordance with Baer's criterion coincide. Also we will look into completeness and stability of a class of principally weakly injective $S$-acts and a class of fg-weakly injective $S$-acts, which are analogs of $p$-injective modules and finitely injective modules.
Keywords: injective $S$-act, weakly injective $S$-act, principally weakly injective $S$-act, fg-weakly injective $S$-act, complete class
Mots-clés : stable class. 
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E. L. Efremov. Completeness and stability of the class of injective. Algebra i logika, Tome 59 (2020) no. 1, pp. 48-65. http://geodesic.mathdoc.fr/item/AL_2020_59_1_a2/

[1] A. A. Stepanova, “Aksiomatiziruemost i polnota klassa in'ektivnykh poligonov nad kommutativnym monoidom i nad gruppoi”, Sib. matem. zh., 56:3 (2015), 650–662 | Zbl

[2] E. L. Efremov, A. A. Stepanova, “Aksiomatiziruemost klassa slabo in'ektivnykh poligonov”, Sib. matem. zh., 58:4 (2017), 785–795 | Zbl

[3] T. G. Mustafin, “O stabilnostnoi teorii poligonov”, Teoriya modelei i ee primenenie, Tr. in-ta matem. SO AN SSSR, 8, Nauka, Novosibirsk, 1988, 92–107

[4] A. V. Mikhalev, E. V. Ovchinnikova, E. A. Palyutin, A. A. Stepanova, “Teoretiko-modelnye svoistva regulyarnykh poligonov”, Fundament. i prikl. matem., 10:4 (2004), 107–157 | Zbl

[5] V. Gould, A. V. Mikhalev, E. A. Palyutin, A. A. Stepanova, “Teoretiko-modelnye svoistva svobodnykh, proektivnykh i ploskikh $S$-poligonov”, Fundament. i prikl. matem., 14:7 (2008), 63–110

[6] Yu. L. Ershov, E. A. Palyutin, Matematicheskaya logika, 6-e izd., Fizmatlit, M., 2011

[7] E. A. Palyutin, “Spektr i struktura modelei polnykh teorii”, Spravochnaya kniga po matematicheskoi logike, v 4-kh chastyakh, v. 1, Teoriya modelei, ed. Dzh. Barvais, Nauka, M., 1982, 320–387

[8] M. Kilp, U. Knauer, A. V. Mikhalev, Monoids, acts and categories. With applications to wreath products and graphs, A handbook for students and researchers, de Gruyter Expo. Math., 29, Walter de Gruyter, Berlin, 2000 | MR | Zbl