Right dc-Noetherian $S$-posets

Document Type : Research Paper

Author

Department of Mathematics, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran

Abstract

In the present paper, the right dc-Noetherianity for $S$-posets is defined and studied. Some fundamental properties of right dc-Noetherian $S$-posets are presented, and the relation of right dc-Noetherian $S$-posets with sub $S$-posets, factor $S$-posets, products, and coproducts are studied. Finally, the relations between right po-Noetherian $S$-posets, right dc-Noetherian $S$-posets and right Noetherian ordered pomonoids are investigated.

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References

[1] Bulman-Fleming, S., & Laan, V. (2005). Lazard's theorem for S-posets, Math. Nachr., 278(15), 1743-1755. https://doi.org/10.1002/mana.200310338
[2] Bulman-Fleming, S. & Mahmoudi, M. (2005). The category of S-posets, Semigroup Forum, 71(3), 443-461. https://doi.org/10.1007/s00233-005-0540-y
[3] Cohn, P. (1968). Universal Algebra, Moscow.
[4] Dandan, Y., Gould, V., Hartmann, M., Rusuk, N., & Zenab, R.E. (2020). Coherency and Construction for Monoids, Quart. J. Math., 71, 1461-1488. https://doi.org/10.1093/qmath/haaa040
[5] Ebrahimi, M.M. & Mahmoudi, M. (2001). The category of M-sets, Ital. J. Pure Appl. Math., 9, 123-132.
[6] Gholipour, A.A., Barzegar, H., Rasouli, H. & Tehranian, A. (2022). S-Acts with  nitely generated universal congruence, Math. Interdisc. Res., 7, 377-384. https://doi.org/10.22052/MIR.2022.246505.1357
[7] Gholipour, A.A., Barzegar, H., Rasouli, H. & Tehranian, A. (2024). S-acts with  nite length on conguences, U.P.B. Sci. Bull., Series A, 86(1), 17-28.
[8] Goodearl, K. & War eld, R. (2004). An introduction to noncommutative noetherian rings, Cambridge University Press.
[9] Gould, V. (1992). Coherent monoids, J. Australian Math. Soc., 53, 166-182. https://doi.org/10.1017/S1446788700035771
[10] Hotzel, E. (1975). On semigroups with maximal conditions, Semigroup Forum, 11, 337-362. https://doi.org/10.1007/BF02195275
[11] Kehayopulu, N. & Tsingelis, M. (2005). Notherian and Artinian Ordered Groupoids-Semigroups, Int. J. Math. Math. Sci. https://doi.org/10.1155/IJMMS.2005.2041.
[12] Khosravi, R. (2017). Rees short exact sequences of S-posets, J. Algebr. Syst., 4(2), 123-134. https://doi.org/10.22044/jas.2017.853
[13] Khosravi, R., & Roueentan, M. (2023). Composition series on (Rees) congruences of S-acts, Categ. Gen. Algebr. Struct. Appl., 19(1), 29-46. https://doi.org/10.48308/cgasa.19.1.29
[14] Khosravi, R., & Roueentan, M. (2024). Chain conditions on (Rees) congruences of S-acts, J. Algebra Appl., 23(05), 2450085. https://doi.org/10.1142/S0219498824500853.
[15] Khosravi, R., Roueentan, M., & Rahimi, E. (2024). Some ramarks on locally Noetherian and locally Artinian S-acts over monoids, Facta Universitatis (NIS): Ser. Math. Inform., 39(3), 439-449. https://doi.org/10.22190/FUMI230711030K
[16] Khosravi, R., Roueentan, M., & Rahimi, E. (2025). On Po-Noetherian S-posets over pomonoids, The 5th National Congress on Mathematics and Statistics.
[17] Kilp, M., Knauer, U., & Mikhalev, A. (2000). Monoids, Acts and Categories, Walter de Gruyter, Berlin, New York.
[18] Kolesnikova, K.A. (2024). Artinian and Noetherian acts over completely 0-Simple semigroups, Mosc. Univ. Math. Bull., 79, 257-261. https://doi.org/10.3103/S0027132224700323
[19] Kozhukhov, I. (1980). On semigroups with minimal or maximal condition on left congruences, Semigroup Forum, 21, 337-350. https://doi.org/10.1007/BF02572558
[20] Miller, C. (2021). Semigroups whose right ideals are  nitely generated, Proc. Edinb.Math. Soc., 64, 848-883. https://doi.org/10.1017/S0013091521000638
[21] Normak, P. (1977). On Noetherian and  nitely presented acts (in Russian), Tartu Ul. Toimetised, 431, 37-46.
[22] Sadhya, S., & Hansda, K. (2022). Generalized Green's relations and GV-ordered semi-groups, Quasigroups Relat. Syst., 30, 161-168. https://doi.org/10.56415/qrs.v30.14
[23] Shahbaz, L. (2023). Finitely presented S-posets, The First National Conference on Applied Researches in Basic Sciences.
[24] Shahbaz, L. (2026). Weakly right po-Noetherian ordered semigroups, Categ. Gen. Algebr. Struct. Appl., 24(1), 151-170. https://doi.org/10.48308/cgasa.24.1.151
[25] Shahbaz, L. (2023). Po-Noetherian posemigroups, The First National Conference on Applied Researches in Basic Sciences.
[26] Shahbaz, L. & Mahmoudi, M. (2014). Various kinds of regular injectivity for S-posets, Bull. Iranian Math. Soc., 40(1), 243-261.
[27] Shahbaz, L. & Mahmoudi, M. (2015). Injectivity of S-posets with respect to down closed regular monomorphisms, Semigroup Forum, 91, 584-600. https://doi.org/10.1007/s00233-014-9676-y
[28] X. Shi, On atness properties of cyclic S-posets, Semigroup Forum, 77 (2008), 248-266. 

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History

  • Receive Date: 18 November 2025
  • Revise Date: 10 February 2026
  • Accept Date: 22 May 2026

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