Principally Left Hereditary and Principally Left Strong Radicals

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: principally left hereditary principally left strong and normal radicals Brown-McCoy and Behrens radicals
• 年，卷（期）: 2001,（4）
• 页码范围: 409-418
• 页数: 10页
• 分类号: O1
• 语种: 英文

摘要

A radical γ is normal if and only if γ is principally left hereditary and principally left strong (i.e., γ(L) = L e A and Lz ∈γ for all z ∈ L imply L γ(A)). Let a radical γ satisfy that A°∈γ and S° A° imply S°∈γ.Then γ is a hereditary normal radical if and only if γ is principally left strong and γ {A | (A, +,◇a) ∈γ a ∈ A}, where the multiplication ◇a is defined by x ◇a y ＝ xay. The Behrens radical class B is the largest principally left hereditary subclass of the Brown-McCoy radical class G. Neither3 nor G is principally left strong.