×
Koppula, Kavitha; Kedukodi, Babushri Srinivas; Kuncham, Syam Prasad

On prime strong ideals of a seminearring. (English) Zbl 1474.16125

Mat. Vesn. 72, No. 3, 243-256 (2020).
Summary: The concepts of prime ideals and corresponding radicals play an important role in the study of nearrings. In this paper, we define different prime strong ideals of a seminearring \(S\) and study the corresponding prime radicals. In particular, we prove that \(P_e=\{S\mid P_e(S)=S\}\) is a Kurosh-Amitsur radical class where \(P_e(S)\) denotes the intersection of equiprime strong ideals of \(S\).

Cited in 5 Documents

MSC:

16Y30 Near-rings
16Y60 Semirings

Keywords:

seminearring; strong ideal; radical
PDF BibTeX XML Cite
\textit{K. Koppula} et al., Mat. Vesn. 72, No. 3, 243--256 (2020; Zbl 1474.16125)
Full Text: Link Link

References:

[1] J. Ahsan,Seminear-rings characterized by their S-ideals. I, Proc. Japan Acad. Ser. A,71(5) (1995), 101-103. · Zbl 0842.16035
[2] J. Ahsan,Seminear-rings characterized by their S-ideals. II, Proc. Japan Acad. Ser. A,71(6) (1995), 111-113. · Zbl 0842.16036
[3] T. Anderson, K. Kaarli, R. Wiegandt,Radicals and subdirect decompositions, Comm. Algebra, 13(2)(1985), 479-494. · Zbl 0553.16004
[4] M. Bataineh, R. Malas,Generalizations of prime ideals over commutative semirings, Math. Vesnik.,66(2)(2014), 133-139. · Zbl 1458.16051
[5] G. Birkenmeier, H. Heatherly, E. Lee,Completely prime ideals and radicals in nearrings in Near-Rings and Near-Fields, Springer publishers, 1995. · Zbl 0839.16040
[6] G.L. Booth, N.J. Groenewald, S. Veldsman,A Kurosh-Amitsur prime radical for near-rings, Comm. Algebra,18(9)(1990), 3111-3122. · Zbl 0706.16025
[7] N.J. Divinsky,Rings and radicals, University of Toronto Press, 1965. · Zbl 0138.26303
[8] M. K. Dubey, P. Sarohe,On(n−1, n)-φ-prime ideals in semirings, Mat. Vesnik.,67(3)(2015), 222-232. · Zbl 1474.16130
[9] B.J. Gardner, R. Wiegandt,Radical theory of rings, CRC Press, 2003. · Zbl 1034.16025
[10] J.S. Golan,Semirings and their Applications, Kluwer Acadamic Publishers, 1999. · Zbl 0947.16034
[11] N.J. Groenewald,The completely prime radical in near-rings, Acta Math. Hung.,51(3-4) (1988), 301-305. · Zbl 0655.16025
[12] B. Jagadeesha, S.P. Kuncham, B.S. Kedukodi,Implications on a Lattice, Fuzzy. Inf. Eng., 8(4)(2016), 411-425.
[13] K. Koppula, B.S. Kedukodi, S.P. Kuncham,On strong ideals of seminearrings, (Communicated).
[14] K.V. Krishna, N. Chatterjee,A necessary condition to test the minimality of generalized linear sequential machines using the theory of near-semirings, Algebra Discrete Math.,4(3)(2005), 30-45. · Zbl 1093.16038
[15] K.V. Krishna, N. Chatterjee,Representation of near-semirings and approximation of their categories, Southeast Asian Bull. Math.,31(2007), 903-914. · Zbl 1140.16309
[16] S.P. Kuncham, B. Jagadeesha, B.S. Kedukodi,Interval valued L-fuzzy cosets of nearrings and isomorphism theorems, Afr. Mat.,27(3)(2016), 393-408. · Zbl 1377.16041
[17] H. Nayak, S.P. Kuncham, B.S. Kedukodi,Extensions of boolean rings and nearrings, Journal of Siberian Federal University - Mathematics and Physics,12(1)(2019), 58-67. · Zbl 07325480
[18] G. Pilz,Near-rings: The Theory and Its Applications, Revised edition, North Hollond, 1983. · Zbl 0521.16028
[19] R.S. Rao, K.S. Prasad,A Kurosh-Amitsur left jacobson radical for right near-rings, Bull. Korean Math. Soc.,45(2008), 457-466. · Zbl 1158.16022
[20] W.G. Van Hoorn, B. Van Rootselaar,Fundamental notions in the theory of seminearrings, Compos. Math.,18(1967), 65-78. · Zbl 0166.03904
[21] S. Veldsman,Modulo-constant ideal-hereditary radicals of nearrings, Quaest. Math.,11 (1988), 253-278. · Zbl 0656.16017
[22] S. Veldsman,On equiprime near-rings, Commun. Algebra.,20(1992), 2569-2587. · Zbl 0795.16034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.