The soft Jacobson radical of a commutative ring

Authors

  • Jayanta Ghosh University of Calcutta
  • Dhananjoy Mandal University of Calcutta
  • Tapas Kumar Samanta Uluberia College

DOI:

https://doi.org/10.52737/18291163-2021.13.11-1-9

Keywords:

Jacobson radical, Jacobson semisimple ring, soft maximal int-ideal, Soft Jacobson radical

Abstract

In this paper, the notion of the soft Jacobson radical of a ring is defined. A relationship between the soft Jacobson radical of a ring and Jacobson semisimple ring is established. Some properties of this notion have been studied under homomorphism.

References

U. Acar, F. Koyuncu, and B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59 (2010), no. 11, pp. 3458-3463. https://doi.org/10.1016/j.camwa.2010.03.034

H. Aktas, and N. Cagman, Soft sets and soft groups, Inform. Sci., 177 (2007), pp. 2726-2735.

M. I. Ali, F. Feng, X. Liu, W. K. Min, and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), no. 9, pp. 1547-1553.

A. O. Atagün, and A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl., 61 (2011), no. 3, pp. 592-601. https://doi.org/10.1016/j.camwa.2010.12.005

N. Cagman, F. Citak, and H. Aktas, Soft int-group and its applications to group theory, Neural Comput. Appl., 21 (2012), pp. 151-158.

Y. Celik, C. Ekiz, and S. Yamak, A new view on soft rings, Hacettepe J. Math. Stat., 40 (2011), no. 2, pp. 273-286.

F. Citak, and N. Cagman, Soft int-rings and its algebraic applications, J. Intell. Fuzzy Syst., 28 (2015), no. 3, pp. 1225-1233.

F. Feng, Y. B. Jun, and X. Zhao, Soft semirings, Comput. Math. Appl., 56 (2008), pp. 2621-2628.

J. Ghosh, D. Mandal, and T. K. Samanta, Soft semiprimary int-ideals of a ring, Analele Universitatii Oradea Fasc. Matematica, 25 (2018), no. 1, pp. 141-151.

J. Ghosh, D. Mandal, and T. K. Samanta, Soft maximal and irreducible int-ideals of a ring, New Math. Nat. Comput., 16 (2020), no. 1, pp. 37-52.

K. Kaygisiz, Homomorphism and isomorphism of soft int-groups, Afr. Mat., 29 (2018), pp. 641-654. https://doi.org/10.1007/s13370-018-0566-4

P. K. Maji and A. R. Roy, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), pp. 1077-1083.

D. S. Malik, J. M. Mordeson, and M. K. Sen, Fundamentals of Abstract Algebra, The McGraw-Hill Companies Inc., 1997.

D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), pp. 19-31.

A. S. Sezer, and A. O. Atagün, A new kind of vector space: Soft vector space, Southeast Asian Bull. Math., 40 (2016), pp. 753-770.

A. S. Sezer, N. Çaǧman, A. O. Atagün, M. I. Ali, and E. Türkmen, Soft intersection semigroups, ideals and bi-ideals; a new application on semigroup theory I, Filomat, 29 (2015), no. 5, pp. 917-946. https://doi.org/10.2298/FIL1505917S

Downloads

Published

2021-12-21

How to Cite

Ghosh, J., Mandal, D., & Samanta, T. K. (2021). The soft Jacobson radical of a commutative ring. Armenian Journal of Mathematics, 13(11), 1–9. https://doi.org/10.52737/18291163-2021.13.11-1-9