Morita equivalence of semirings with local units
Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 37-60.

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In this paper we study some necessary and sufficient conditions for two semirings with local units to be Morita equivalent. Then we obtain some properties which remain invariant under Morita equivalence.
Keywords: semiring, semimodule.
Mots-clés : Morita equivalence, Morita context, Morita invariant
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M. Das; S. Gupta; S. K. Sardar. Morita equivalence of semirings with local units. Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 37-60. http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a2/

[1] G. D. Abrams, “Morita equivalence for rings with local units”, Communications in Algebra, 11:8 (1983), 801–837 | DOI | MR | Zbl

[2] J. Adamek, H. Herlich and G. Strecker, Abstract and concrete categories, John Wiley Sons, New York, 1990 | MR | Zbl

[3] F. W. Anderson and K. R. Fuller, Rings and categories of modules, 2nd ed., Springer, New York, 1992 | MR | Zbl

[4] P. N. Ánh and L. Márki, “Morita equivalence for rings without identity”, Tsukuba J. Math., 11:1 (1987), 1–16 | MR | Zbl

[5] S. Ghosh, “A characterization of ring congruences on semirings”, Soochow J. Math., 19:3 (1993), 305–312 | MR | Zbl

[6] J. S. Golan, Semirings and Their Applications, Kluwer Academic Publishers, Dordrecht, 1999 | MR | Zbl

[7] U. Hebisch and H. J. Weinert, Semirings: Algebraic Theory and Applications in Computer Science, World Scientific Publishing, Singapore, 1998 | MR | Zbl

[8] U. Hebisch and H. J. Weinert, “Semirings and semifields”, Handbook of Algebra, v. 1, 1996, 425–462 | DOI | MR | Zbl

[9] M. Kilp, U. Knauer and A. V. Mikhalev, Monoids, acts and categories, Walter de Gruyter, Berlin–New York, 2000 | MR | Zbl

[10] Y. Katsov and T. G. Nam, “Morita equivalence and homological characterization of semirings”, Journal of Algebra and Its Applications, 10:3 (2011), 445–473 | DOI | MR | Zbl

[11] Y. Katsov, T. G. Nam and J. Zumbragel, “On simpleness of semirings and complete semirings”, J. Algebra Appl., 13:6 (2014), 1450015, 29 pp. | DOI | MR | Zbl

[12] S. Mac Lane, Categories for the Working Mathematician, Springer, New York, 1971 | MR | Zbl

[13] K. Morita, “Duality of modules and its applications to the theory of rings with minimum condition”, Science Rep. Tokyo Kyoiku Daigaku Sect. A6, 1958, 85–142 | MR

[14] T. K. Mukherjee, M. K. Sen and S. Ghosh, “Chain conditions on semirings”, International Journal of Mathematics and Mathematical Sciences, 19:2 (1996), 321–326 | DOI | MR | Zbl

[15] S. K. Sardar, S. Gupta and B. C. Saha, “Morita equivalence of semirings and its connection with Nobusawa $\Gamma$-semirings with unities”, Algebra Colloquium, 22, Spec 1 (2015), 985–1000 | DOI | MR | Zbl

[16] S. K. Sardar and S. Gupta, “Morita invariants of semirings”, J. Agebra Appl., 15:2 (2016), 1650023, 14 pp. | DOI | MR | Zbl

[17] S. K. Sardar and S. Gupta, “Morita invariants of semirings-II”, Asian-European Journal of Mathematics, 11:1 (2018), 1850014 | DOI | MR | Zbl