PRME AND k-PRIME IDEALS IN Ω-GROUPS
作者:
A. Buys,
G.K. Gerber,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1985)
卷期:
Volume 8,
issue 1
页码: 15-32
ISSN:1607-3606
年代: 1985
DOI:10.1080/16073606.1985.9631897
出版商: Taylor & Francis Group
关键词: Primary 201399 Secondary 16A12;16A22;08A99;17A65
数据来源: Taylor
摘要:
In this paper we define two concepts of prime ideals for Ω-groups. The first generalizes the definitions of prime ideal in rings, nearrings, Γ-rings, associative algebras and Lie algebras. The second generalizes a concept defined for groups by Ščukin ([21]). We show that both lead to radicals in the sense of Hoehnke ([10]). Furthermore in the case of rings, Γ-rings, abelian zero-symmetric nearrings and cubic rings these two definitions coincide, thus obtaining a new characterization for the prime ideal. Zero-symmetric Ω-groups are defined analogously to the nearring case and a new characterization in term of ideals is given.
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