The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R0[x] equals to the set of all nilpotent elements of R0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R0[x] is a subset of the intersection of all maximal left ideals of R0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R0[x] coincides with the intersection of all maximal left ideals of R0[x]. Moreover, we prove that the quasi-radical of R0[x] is the greatest quasi-regular (right) ideal of it.
Beidleman, J. C., Quasi-regularity in near-rings, Mathematische Zeitschrift89 (1965), 224–229.
Beidleman, J. C., Quasi-regularity in near-rings, Mathematische Zeitschrift89 (1965), 224–229.)| false
Regional discounts on country of the funding agency
World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Online subsscription: 672 EUR / 840 USD
Print + online subscription: 760 EUR / 948 USD
Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title
Individual articles are sold on the displayed price.
Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
H-1051 Budapest, Hungary, Széchenyi István tér 9.
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.