Composition series on (Rees) congruences of S-acts.

Khosravi, Roghaieh; Roueentan, Mohammad

doi:10.48308/cgasa.19.1.29

	Composition series on (Rees) congruences of S-acts.
Categories and General Algebraic Structures with Applications
مقاله 3، دوره 19، شماره 1، آبان 2023، صفحه 29-46 اصل مقاله (489.65 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.48308/cgasa.19.1.29
نویسندگان
Roghaieh Khosravi¹؛ Mohammad Roueentan²
¹Department of Mathematics, Faculty of Sciences, Fasa University, Fasa, Iran.
²College of Engineering, Lamerd Higher Education Center, Lamerd, Iran.
چکیده
In this paper, we study composition series of subacts or congruences of S-acts. It is shown that composition series of subacts are exactly those that are both Rees artinian and Rees noetherian, i.e. those satisfying both ascending and descending chain conditions on subacts. But this is not valid for the case of composition series of congruences in general. We prove that the properties of having composition series of subacts or congruences are inherited in Rees short exact sequences. Also, we discuss whenever two composition series of subacts or congruences have the same length and they are equivalent.
کلیدواژه‌ها
(Rees) Noetherian؛ (Rees) Artinian؛ composition series

مراجع
[1] Anderson, A. and Fuller, K., “Rings and Categories of Modules”, Springer-Verlag, 1992. [2] Dandan, Y., Gould, V., Hartmann M., Rusuk N., and Zenab R.E., Coherency and construction for monoids, Quart. J. Math. 71 (2020), 1461-1488. [3] Davvaz, B. and Nazemian, Z., Chain conditions on commutative monoids, Semigroup Forum 100 (2020), 732-742. [4] Estaji, A.A. and Shabani, M., A note on multiplication S-acts, Far East J. Math. Sci. 36(2) (2010), 133-150. [5] Gould, V., Coherent monoids, J. Australian Math. Soc. 53 (1992), 166-182. [6] Hotzel, E., On semigroups with maximal conditions, Semigroup Forum 11 (1975), 337-362. [7] Kilp, M., Knauer, U., and Mikhalev, A., “Monoids, Acts and Categories”, Walter de Gruyter, 2000. [8] Kozhukhov, I., On semigroups with minimal or maximal condition on left congru- ences, Semigroup Forum 21 (1980), 337-350. [9] Kozkukhov, I., Semigroups with certain conditions on congruences. J. Math. Sci. 114 (2003), 1119-1126. [10] Khosravi, R. and Roueentan, M., Co-uniform and hollow S-acts over monoids, Commun. Korean Math. Soc. 37(2) (2022), 347-358. [11] Khosravi, R., Liang, X., and Roueentan, M., On Cogenerating and finitely cogenerated S-acts, https://arxiv.org/abs/2109.00344. [12] Khosravi, R. and Roueentan, M., Chain conditions on (Rees) congruences of S-acts, J. Algebra Appl., https://doi.org/10.1142/S0219498824500853. [13] Miller, C. and Rusuk, N., Right Noetherian semigroups, Int. J. Algebra Comput. 30 (2020), 13-48. [14] Wisbauer, R., “Foundations of module and ring theory” , Gordon and Breach Science Publishers, 1991. [15] Barzegar, H., Essentiality in the category of S-acts, Eur. J. Pure App. Math. 9(1) ( 2016), 19-26. [16] Chen, Y. and Shum, K.P., Rees short exact sequences of S-systems, Semigroup Forum 65 (2002), 141-148. [17] Roueentan, M. and Sedaghatjoo, M., On uniform acts over semigroups, Semigroup Forum 97 (2018), 229-243.
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Composition series on (Rees) congruences of S-acts.