摘要
本文讨论弱对称near-环,它是以零对称near-环作为特殊情形的一类near-环,对于弱对称near-环,证明了J_ν={N|N～N′≠{0}■J_ν(N′)≠{0}},ν∈{2,*,3}是Amitsur-Kurosh意义下的Jacobson-型根环类(简称“J-型根环类”),从而突破了J-型根环类局限于零对称near-环的范围。另外,对于一般near-环,证明了J.真介于J_5/2与J_3之间。
This paper discusses the weak-symmetric near ring.It is a class of rings witho-symmetric near-rings as a particular case.As for the weak-symmetric near-ring,we have proved J_v={N N～N′≠{0}■J_v(N′)≠={0}},v∈{2,*,3}is a classof Jacobson-type radical(abbreviation for“the class of J-type radical”)in Amitsur-Kurosh's meaning,thus it breaks through the range of the class of J-type radicalrestricted to the 0-symmetric near-ring.Besides,we have proved J_(5/2) is betweenJ.and J_3 for the general near-ring.
出处
《晓庄学院自然科学学报》
CAS
1991年第2期97-101,共5页
Journal of Natural Science of Hunan Normal University
关键词
near-环
环
理想
Jacobson根基
ring
ideal(mathematics)
primitive ring
primitive ideal
Jacobson radical near-rings
