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Natural Sciences Issue (Vietnamese)
Date Published:
03/05/2026
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How to Cite
Pham, Q. T., & Le, H. M. (2026). The Js - semisimple semirings. Dong Thap University Journal of Science, Online First, 1-10. https://doi.org/10.52714/dthu.ns.2941.1899
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The Js - semisimple semirings
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Abstract
In this paper, we extend Proposition 11.1 (Lam, 2001) to characterize the class of Js-semisimple semirings. By applying the obtained results, we investigate the properties of Js-semisimple semirings in relationship to simple semimodules. Finally, we provide some examples of Js-semisimple semirings to illustrate these results.
Keywords
Js-radical of semiring, Js-semisimple semiring, Simple semimodules
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
Bourne, S. (1951). The Jacobson radical of a semiring. Proc. Nat. Acad. Sci. U.S.A, 37, 163 – 170. https://www.pnas.org/doi/10.1073/pnas.37.3.163.
Gardner, J., & Wiegandt, R. (2004). Radical theory of rings. Marcel Dekker,
Inc., New York, Basel.
Golan, J. (1999), Semirings and their applications, Kluwer Academic Publishers, Dordrecht-Boston-London.
Iizuka, K. (1959). On the Jacobson radical of a semiring, Tohoku Math. J., 11(2), 409 - 421. https://projecteuclid.org/journals/tohoku-mathematical-journal/volume-11/issue-3.
Jacobson, N. (1945). The radical and semi-simplicity for arbitrary rings. American Journal of Mathematics, 67(2), 300–320. https://doi.org/10.2307/2371731.
Katsov, Y., & Nam, T. G. (2014). On radicals of semirings and related problems. Communications in Algebra, 42(12), 5065–5099. https://doi.org/10.1080/00927872.2013.833208.
Lam, T. Y. (2001). A first course in noncommutative rings (2nd ed.). Springer. https://doi.org/10.1007/978-1-4419-8616-0.
Latorre, D. R. (1965). A note on the Jacobson radical of a hemiring. Publ. Math. (Debrecen), 14, 9 - 13.
Mai, L. H., & Tuyen, N. X. (2016). On Js-semisimple left (right) V-semirings. J. Adv. Math. Stud., 9(3), 437 - 443.
Mai, L. H., & Tuyen, N. X. (2017). Some remarks on the Jacobson radical types of semirings and related problems. Vietnam Journal of Mathematics, 45(3), 493–506.
https://doi.org/10.1007/s10013-016-0226-7.
Vandiver, H. S. (1934). Note on a simple type of algebra in which the cancellation law of addition does not hold. Bull. Am. Math. Soc., 40, 914-920.
https://www.ams.org/journals/bull/1934-40-12/S0002-9904-1934-06003-8/
Gardner, J., & Wiegandt, R. (2004). Radical theory of rings. Marcel Dekker,
Inc., New York, Basel.
Golan, J. (1999), Semirings and their applications, Kluwer Academic Publishers, Dordrecht-Boston-London.
Iizuka, K. (1959). On the Jacobson radical of a semiring, Tohoku Math. J., 11(2), 409 - 421. https://projecteuclid.org/journals/tohoku-mathematical-journal/volume-11/issue-3.
Jacobson, N. (1945). The radical and semi-simplicity for arbitrary rings. American Journal of Mathematics, 67(2), 300–320. https://doi.org/10.2307/2371731.
Katsov, Y., & Nam, T. G. (2014). On radicals of semirings and related problems. Communications in Algebra, 42(12), 5065–5099. https://doi.org/10.1080/00927872.2013.833208.
Lam, T. Y. (2001). A first course in noncommutative rings (2nd ed.). Springer. https://doi.org/10.1007/978-1-4419-8616-0.
Latorre, D. R. (1965). A note on the Jacobson radical of a hemiring. Publ. Math. (Debrecen), 14, 9 - 13.
Mai, L. H., & Tuyen, N. X. (2016). On Js-semisimple left (right) V-semirings. J. Adv. Math. Stud., 9(3), 437 - 443.
Mai, L. H., & Tuyen, N. X. (2017). Some remarks on the Jacobson radical types of semirings and related problems. Vietnam Journal of Mathematics, 45(3), 493–506.
https://doi.org/10.1007/s10013-016-0226-7.
Vandiver, H. S. (1934). Note on a simple type of algebra in which the cancellation law of addition does not hold. Bull. Am. Math. Soc., 40, 914-920.
https://www.ams.org/journals/bull/1934-40-12/S0002-9904-1934-06003-8/
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