JP Journal of Algebra, Number Theory and Applications

The JP Journal of Algebra, Number Theory and Applications is a prestigious international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research papers, both theoretical and applied in nature, in various branches of algebra and number theory. The journal also welcomes survey articles that contribute to the advancement of these fields.

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COMMUTATIVITY OF HYPERRINGS WITH REVERSE DERIVATIONS

Authors

  • G. Basavaraju
  • Sk. Haseena
  • C. Jaya Subba Reddy

Keywords:

hyperrings, prime hyperring, hyperideal, reverse derivation

DOI:

https://doi.org/10.17654/0972555524033

Abstract

In this paper, we introduce the notion of reverse derivation on Krasner hyperrings and investigate some of their properties. Also, we obtain some properties of reverse derivation on a prime Krasner hyperring which proves the commutativity of a Krasner hyperring.

Received: July 26, 2024
Revised: August 12, 2024
Accepted: October 10, 2024

References

A. Asokkumar, Derivation in hyperrings and prime hyperrings, Iranian Journal of Mathematical Sciences and Informatics 8(1) (2013), 1-13.

H. E. Bell and L. C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar. 53 (1989), 339-346.

M. Bresar, On the distance of the compositions of two derivations to the generalized derivations, Glasg. Math. J. 33(1) (1991), 89-93.

M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385-394.

M. Bresar and J. Vukman, On some additive mapping in rings with involution, Aeq. Math. 38 (1989), 178-185.

B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.

B. Davvaz and T. Vougiouklis, Commutative rings obtained from hyperrings with -relations, Comm. Algebra 35 (2007), 3307-3320.

I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110.

C. Jaya Subba Reddy and K. Hemavathi, Reverse derivations on semiprime rings, Ultra Scientist of Physical Sciences (International Journal of Physical Sciences) 26(1)A (2014), 111-113.

C. Jaya Subba Reddy and K. Hemavathi, Some results on reverse derivations in prime rings, Mathematical Sciences International Research Journal 3(2) (2014), 734-735.

C. Jaya Subba Reddy and K. Hemavathi, Reverse derivations in prime rings, International Journal of Research in Electronics and Computer Engineering 2(1) (2014), 28.

C. Jaya Subba Reddy, S. Mallikarjuna Rao and V. Vijaya Kumar, Centralizing and commuting left generalized derivations on prime rings, Int. J. Bull. Math. Sci. Appl. 11 (2015), 1-3.

L. Kamali and B. Davvaz, Some notes on differential hyperrings, Iranian Journal of Science and Technology 39A1 (2015), 101-111.

M. Krasner, A class of hyperrings and hyperfields, Int. J. Math. Math. Sci. 6 (1983), 307-311.

F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandenaves, Stockholm, 1934, pp. 45-49.

E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.

M. Samman and N. Alyamani, Derivations and reverse derivations in semiprime rings, Int. J. Forum 39(2) (2007), 1895-1902.

Published

2024-10-23

Issue

Section

Articles

How to Cite

COMMUTATIVITY OF HYPERRINGS WITH REVERSE DERIVATIONS. (2024). JP Journal of Algebra, Number Theory and Applications, 63(6), 615-626. https://doi.org/10.17654/0972555524033

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