In this paper, some properties of soft radical of a soft int-ideal have been developed and soft prime int-ideal, soft semiprime int-ideal of a ring are defined. Several characterizations of soft prime (soft semiprime) int-ideals are investigated. Also it is shown that the direct and inverse images of soft prime (soft semiprime) int-ideals under homomorphism remains invariant.
Citation: Jayanta Ghosh, Dhananjoy Mandal, Tapas Kumar Samanta. Soft prime and semiprime int-ideals of a ring[J]. AIMS Mathematics, 2020, 5(1): 732-745. doi: 10.3934/math.2020050
In this paper, some properties of soft radical of a soft int-ideal have been developed and soft prime int-ideal, soft semiprime int-ideal of a ring are defined. Several characterizations of soft prime (soft semiprime) int-ideals are investigated. Also it is shown that the direct and inverse images of soft prime (soft semiprime) int-ideals under homomorphism remains invariant.
| [1] |
L. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X
|
| [2] |
Z. Pawlak, Rough sets, Int. J. Inform. Comput. Sci., 11 (1982), 341-356. doi: 10.1007/BF01001956
|
| [3] | D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19-31. |
| [4] |
H. Aktas, N. Cagman, Soft sets and soft groups, Inform. Sci., 177 (2007), 2726-2735. doi: 10.1016/j.ins.2006.12.008
|
| [5] |
U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59 (2010), 3458-3463. doi: 10.1016/j.camwa.2010.03.034
|
| [6] |
A. O. Atagun, A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl., 61 (2011), 592-601. doi: 10.1016/j.camwa.2010.12.005
|
| [7] |
F. Feng, Y. B. Jun, X. Zhao, soft semirings, Comput. Math. Appl., 56 (2008), 2621-2628. doi: 10.1016/j.camwa.2008.05.011
|
| [8] |
X. Liu, D. Xiang, J. Zhan, et al. Isomorphism theorems for soft rings, Algebra Colloquium, 19 (2012), 649-656. doi: 10.1142/S100538671200051X
|
| [9] |
Q. M. Sun, Z. L. Zhang, J. Liu, Soft sets and soft modules, Lecture Notes in Comput. Sci., 5009 (2008), 403-409. doi: 10.1007/978-3-540-79721-0_56
|
| [10] |
A. Aygunoglu, H. Aygun, Introduction to fuzzy soft groups, Comput. Math. Appl., 58 (2009), 1279-1286. doi: 10.1016/j.camwa.2009.07.047
|
| [11] | Y. Celik, C. Ekiz, S. Yamak, Applications of fuzzy soft sets in ring theory, Ann. Fuzzy Math. Inform., 5 (2013), 451-462. |
| [12] |
F. Feng, C. Li, B. Davvaz, et al. Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Comput. 14 (2010), 899-911. doi: 10.1007/s00500-009-0465-6
|
| [13] | J. Ghosh, B. Dinda, T. K. Samanta, Fuzzy soft rings and fuzzy soft ideals, Int. J. Pure Appl. Sci. Technol. 2 (2011), 66-74. |
| [14] |
X. Liu, D. Xiang, J. Zhan, Fuzzy isomorphism theorems of soft rings, Neural Comput. Appl., 21 (2012), 391-397. doi: 10.1007/s00521-010-0439-8
|
| [15] |
N. Cagman, F. Citak, H. Aktas, Soft int-group and its applications to group theory, Neural Comput. Appl., 21 (2012), 151-158. doi: 10.1007/s00521-011-0752-x
|
| [16] |
N. Cagman, F. Citak, Soft int-rings and its algebraic applications, J. Intell. Fuzzy Syst., 28 (2015), 1225-1233. doi: 10.3233/IFS-141406
|
| [17] | J. Ghosh, D. Mandal, T. K. Samanta, Soft semiprimary int-ideals of a ring, Analele Universitatii Oradea Fasc. Matematica, 2 (2018), 141-151. |
| [18] |
A. S. Sezer, N. Cagman, A. O. Atagun, et al. Soft Intersection Semigroups, Ideals and Bi-Ideals; a New Application on Semigroup Theory I, Filomat, 29 (2015), 917-946. doi: 10.2298/FIL1505917S
|
| [19] |
M. I. Ali, F. Feng, X. Liu, et al. On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547-1553. doi: 10.1016/j.camwa.2008.11.009
|
| [20] | D. M. Burton, First Course in Rings and Ideals, Addison-Wesley series in Mathematics, 1970. |
Jayanta Ghosh, Dhananjoy Mandal, Tapas Kumar Samanta. Soft prime and semiprime int-ideals of a ring[J]. AIMS Mathematics, 2020, 5(1): 732-745. doi: 10.3934/math.2020050
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