On k-Noetherian and k-Artinian semirings
*Jawad AbuhlailCorresponding authorabuhlail@kfupm.edu.saDepartment of MathematicsCollege of Computing and MathematicsKing Fahd University of Petroleum & MineralsDhahran, 31261, Saudi ArabiaView full profile → , Rangga Ganzar Noegraharangga.gn@universitaspertamina.ac.idDepartment of Actuarial ScienceCollege of Sciences and ComputerUniversitas PertaminaJakarta, 12220, IndonesiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Jul 2025
- Published Online:
- 13 Mar 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2626
- Pages:
- 1485–1501
Abstract
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References
[1] F. Alarcon and D. Anderson, “Commutative semirings and their lattices of ideals”, Houston J. Math., vol. 20, pp. 571-590 (1994).
[2] J. Y. Abuhlail and R. G. Noegraha, “Injective Semimodules - Revisited”, J. Algebra Appl., vol. 21, no. 1, Article ID 2250242, 28 pp. (2022).
[3] J. Abuhlail, “Exact sequence of commutative monoids and semimodules”, Homology Homotopy Appl., vol. 16, no. 1, pp. 199-214 (2014).
[4] P. J. Allen and L. Dale, “ Ideal theory in Z+” , Publ. Math. Debrecen, vol. 22, no. 3-4, pp. 219-224 (1975).
[5] J. Abuhlail, S. Il’in , Y. Katsov and T. Nam, “ Toward homological characterization of semirings by e-injective semimodules” , J. Algebra Appl., vol. 17, no. 4, 1850059 (24 pages) (2018).
[6] H. Al-Thani, “Injective semimodules”, J. Inst. Math. Comput. Sci., vol. 16, no. 3, pp. 143-152 (2003).
[7] J. Adámek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories; The Joy of Cats. Dover: Dover Publications Edition (2009).
[8] R. Ebrahimi Atani and S. Ebrahimi Atani, “Ideal theory in commutative semirings”, Bul. Acad. Stiinte Repub. Mold. Mat., vol. 57, no. 2, pp. 14-23 (2008).
[9] R. El Bashir, J. Hurt, A. Jancarik abd T. Kepka, “ Simple commutative semirings” , J. Algebra, vol. 236, no. 1, pp. 277-306 (2001).
[10] K. Gł azek, A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences. With Complete Bibliography. Dordrecht: Kluwer Academic Publishers (2002).
[11] J. Golan, Semirings and their Applications. Dordrecht: Kluwer Academic Publishers (1999).
[12] P. A. Grillet, Abstract Algebra. Second Edition, New York: Springer (2007).
[13] M. Henriksen, “ Ideals in semirings with commutative addition” , Notices Amer. Math. Soc., vol. 5, no. 3, pp. 321 (1958).
[14] U. Hebisch and H. J. Weinert, Semirings: Algebraic Theory and Applications in Computer Science. River Edge, NJ: World Scientific Publishing Co., Inc. (1998).
[15] P. Lescot, “Prime and primary ideals in semirings”, Osaka J. Math., vol. 52, no. 3, pp. 721-736 (2015).
[16] S. N. Il’in, “ Direct sums of injective semimodules and direct products of projective semimodules over semirings” , Russ. Math., vol. 54, no. 10, pp. 27-37 (2010).
[17] Y. Katsov, T. G. Nam and N. X. Tuyen, “ More on subtractive semirings: simpleness, perfectness, and related problems” , Comm. Algebra, vol. 39, no. 11, pp. 4342-4356 (2011).
[18] G. L. Litvinov and V. P. Maslov, Idempotent Mathematics and Mathematical Physics, In Contemporary Mathematics, vol. 377, American Mathematical Society, Providence, RI, 2005. Papers from the International Workshop held in Vienna, February 3-10 (2003).
[19] J. Rotman, An Introduction to Homological Algebra, Second edition, New York: Springer (2009).
[20] M. Takahashi, “On the bordism categories. III. Functors Hom and for semimodules”, Math. Sem. Notes Kobe Univ., vol. 10, no. 2, pp. 551-562 (1982).
[21] M. Takahashi, “Extensions of Semimodules I”, Math. Sem. Notes Kobe Univ., vol. 10, pp. 563-592 (1982).
[22] R. Wisbauer, Foundations of Module and Ring Theory: A Handbook for Study and Research. Reading: Gordon and Breach (1991).




