• Communications of the Korean Mathematical Society
• /
• v.12 no.1
• /
• pp.27-36
• /
• 1997

A matrix whose entries consist of the symbols +, -, 0 is called a sign-pattern matrix. We characterize the $n \times n$ irreducible sign-pattern matrices that are sign tripotent.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.541-547
• /
• 2008

Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with $n\;{\geq}\;3$. We denote by $M_n(R)$ the ring of all $n{\times}n$ matrices over R. Let ($J_n(R)$) be the additive subgroup of $M_n(R)$ generated additively by all idempotent matrices. Let ($D=J_n(R)$) or $M_n(R)$. In this paper, by using an additive idem potence-preserving result obtained by Coo (see [4]), I characterize (i) the additive preservers of tripotence from D to $M_m(R)$ when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from $M_n(R)$ to $M_n(R)$ when 2 and 3 are units of R.