A special case of an operator ring, when the domain of operators is a commutative associative ring with unit.
This phrase is not used in the Western literature in the sense indicated. Linear algebra is the theory of (finite-) dimensional vector spaces and linear operators between them. See the entry Linear algebra below.
Linear-algebra(2). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear-algebra(2)&oldid=13344