Open AccessON RINGS SATISFYING BOTH OF 1-abc AND 1-cba BEING INVERTIBLE OR NONE
Author(s) -
Chen-Te Yen
Publication year - 1993
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.24.1993.4503
Subject(s) - invertible matrix , mathematics , integer (computer science) , combinatorics , identity (music) , ring (chemistry) , property (philosophy) , discrete mathematics , pure mathematics , computer science , physics , philosophy , chemistry , organic chemistry , epistemology , acoustics , programming language
Let $R$ be a ring with identity 1 and $n$ a positive integer. We define the property Pn as follows:
(Pn) If $1- a_1a_2a_3 \cdots a_{n-1}a_n$ is invertible in $R$, then so is $1- a_na_2a_3 \cdots a_{n-1}a_1$.
Thus, $R$ satisfies (Pn), for some $n \ge 3$ if and only if $R$ satisfies (P3). Some properties of rings satisfying (P3) are obtained, e.g., $R$ must be directly finite.