[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b170799

UNITS, NILPOTENT ELEMENTS, AND UNIT-IFP RINGS

Park, Sangwon (Department of Mathematics Dong-A University)
Yun, Sang Jo (Department of Mathematics Dong-A University)

Publication Information

Bulletin of the Korean Mathematical Society / v.55, no.5, 2018 , pp. 1389-1396 More about this Journal

Abstract

We observe the structure of a kind of unit-IFP ring that is constructed by Antoine, in relation with units and nilpotent elements. This article concerns the same argument in a more general situation, and study the structure of one-sided zero divisors in such rings. We also provide another kind of unit-IFP ring.

Keywords

unit-IFP ring; unit; nilpotent element; Antoine's construction;

Citations & Related Records

Reference

1	R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra 319 (2008), no. 8, 3128-3140. DOI
2	H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), 363-368. DOI
3	G. M. Bergman, Modules over coproducts of rings, Trans. Amer. Math. Soc. 200 (1974), 1-32. DOI
4	C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761. DOI
5	H. K. Kim, T. K. Kwak, Y. Lee, and Y. Seo, Insertion of units at zero products, J. Algebra Appl. 16 (2018), 1850043, 20 pages.
6	H. K. Kim, T. K. Kwak, Y. Lee, and Y. Seo, Corrigendum to \Insertion of units at zero products [J. Algebra Appl. 16 (2018), no. 11, 1850043, 20 pages]", J. Algebra Appl. 17 (2018), 1892002, 2 pages. DOI
7	Y. Lee, Structure of unit-IFP rings, submitted.