On Commutativity of Near-Rings with Outer \((\sigma ,\tau)\)-\(n\)-derivations

Utsanee Leerawat, Pitipong Aroonruviwat


In this paper we investigate some appropriate conditions involving outer \((\sigma ,\tau)\)-\(n\)-derivations for a near ring to be a commutative ring.


Derivations; Rings; Near-rings; Prime rings; Commutative

Full Text:



P. Aroonruviwat and U. Leerawat, On outer (¾,¿)-n-derivations and commutativity in prime nearrings, International Journal of Mathematics and Computer Science 16(2) (2021), 563 – 575, URL: http://ijmcs.future-in-tech.net/16.2/R-Leerawat-Aroonruviwat.pdf.

M. Ashraf and M. A. Siddeeque, On (¾,¿))-n-derivations in near-rings, Asian-European Journal of Mathematics 6(4) (2013), 1350051 (14 pages), DOI: 10.1142/S1793557113500514.

M. Ashraf, A. Ali and S. Ali, (¾,¿)-derivations on prime near rings, Archivum Mathematicum 40(3) (2004), 281 – 286, URL: https://dml.cz/bitstream/handle/10338.dmlcz/107910/ArchMathRetro_040-2004-3_8.pdf?sequence=1.

R. Balakrishnan and S. Suryanarayanan, P(r,m) near-rings, Bulletin of the Malaysian Mathematical Science Society (Second series) 23(1-4) (2000), 117 – 130, URL: http://math.usm.my/bulletin/pdf/v23n2/v23n2p3.pdf.

H. E. Bell, Near rings in which each element is a power of itself, Bulletin of the Australian Mathematical Society 2 (1970), 363 – 368, DOI: 10.1017/S0004972700042052.

H. E. Bell and G. Mason, On derivations in near-rings, North-Holland Mathematics Studies 137 (1987), 31 – 35, DOI: 10.1016/S0304-0208(08)72283-7.

T. Boykett and G. Wendt, Units in near-rings, Communications in Algebra 44(4) (2016), 1478 – 1495, URL: https://www.tandfonline.com/doi/abs/10.1080/00927872.2015.1012674.

J. R. Clay, Nearrings: Geneses and Applications, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1992), URL: https://global.oup.com/academic/product/nearrings-geneses-and-applications-9780198533986?cc=jp〈=en&.

G. Ferrero, Nearrings: Some Developments Linked to Semigroups and Groups, Advance in Mathematics Series 4, Kluwer Academic Publishers, Dordrecht (2002), DOI: 10.1007/978-1-4613-0267-4.

J. D. P. Meldrum, Near-rings and their links with groups, in: Research Notes in Mathematics 134, Pitman Advanced Publishing Program, Boston, London, Melbourne (1985), https://ur.b-ok.global/book/2363011/61bf2e.

G. Pilz, Near-rings, the Theory and its Applications, 2nd edition, North-Holland, Mathematics Studies, 23, Amsterdam (1983), https://www.elsevier.com/books/near-rings-the-theoryand-its-applications/pilz/978-0-7204-0566-8.

X. K. Wang, Derivations in prime near-rings, Proceedings of the American Mathematical Society 121 (1994), 361 – 366, DOI: 10.2307/2160409.

DOI: http://dx.doi.org/10.26713%2Fcma.v12i1.1473


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905