单边EXCHANGE环(英文)

On One-sided Exchange Rings

本文引进研究了单边Exchange环和Meta-sidedExchange环，给出了单边Exchange环的一类等价条件，得到了约化条件下这几类环的等价性，证明了单边EXCHANGE环上模的直和消去也等价干部分单位正则性．

In this paper,we introduce one-sided exchange ring and mata-sided exchange ring and give some equivalent characterizations under which every ring is a one-sided exchange ring. We also prove that cancellation from direct sums is equvialent to partially unit-regularity over one-sided exchange ring.