Geodesic
Projective and injective unars
Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 107-119.

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In this paper we study projective and injective unars, as well as unars that satisfy conditions that are weakenings of the concepts of projectivity and injectivity. Namely, an algebraic description of projective, weakly-, quasi- and pseudo-projective, injective, weakly-, quasi- and pseudo-injective unars is given. 
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I. A. Sakharov. Projective and injective unars. Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 107-119. http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a9/

[1] Kilp M., Knauer U., Mikhalev A. V., Monoids, acts and categories: With applications to wreath products and graphs. A handbook for students and researchers, Walter de Gruyter, 2000, 539 pp. | MR | Zbl

[2] Berthiaume P., “The injective envelope of S-sets”, Canad. Math. Bull., 10:2 (1967), 261–273 | DOI | MR | Zbl

[3] Feiler E. H., Gantos R. L., “Indecomposable and injective S-systems with zero”, Math. Nachr., 41 (1969), 37–48 | DOI | MR

[4] Yan T., “Generalized injective S-acts on a monoid”, Adv. Math., 40:4 (2011), 421–432 | MR | Zbl

[5] Chen Y., “Projective S-acts and Exact Functors”, Algebra Colloq., 7 (2000), 113–120 | DOI | MR | Zbl

[6] Chen Y., Shum K. P., “Projective and indecomposable S-acts”, Science in China Series A: Mathematics, 42 (1999), 593–599 | DOI | MR | Zbl

[7] Satyanarayana M., “Quasi- and weakly-injective S-systems”, Math. Nachr., 71 (1976), 183–190 | DOI | MR | Zbl

[8] Shaymaa A., Generalizations of quasi injective systems over monoids, University of Al-Mustansiriyah, Baghdad, Iraq, 2015

[9] Jungabel E., Masulovic D. “Homomorphism-homogeneous monounary algebras”, Mathematica Slovaca, 63:5 (2013), 993–1000 | DOI | MR | Zbl

[10] Abbas M. S., Shaymaa A., “Pseudo injective and pseudo QP-injective S-systems over monoids”, International Journal of Pure and Engineering Mathematics (IJPEM), 3:2 (2015), 33–49

[11] Knauer U., Oltmanns H., “Weak projectivities for S-acts”, General Algebra and Discrete Mathematics, 1999, 143–159

[12] Knauer U., Oltmanns H., “On Rees weakly projective right acts”, Fundamentalnaya i Prikladnaya Matematika, 10:3 (2004), 85–96 | MR | Zbl

[13] Roueentan M., Ershad. M., “Quasi-projective covers of right S-acts”, Categories and algebraic structures with applications, 2:1 (2014), 37–45 | MR | Zbl

[14] Zhongkui L., Ahsan J., “On relative Quasi-Projective acts over monoids”, Arabian journal for science and engineering yr 2010, 35:2 | MR

[15] Jungabel E., Quasi-projective monounary algebras, Prepr./ Eotvos Lorand University, 2020, 20 pp.

[16] Skornyakov L. A., Elementy obschei algebry, Nauka, 1983 | MR