Г-环具有强单位元的条件

The Conditions Under Which Γ-rings Have Strong Unity

Kyuno,S.教授在1985年奥地利“国际根的理论与应用会议”上作了“环和根”的报告论证了三个重要定理,其中二个是:具有乘法单位元的结合环范畴与具有乘法强单位元的环范畴是等价的;Morita context环范畴与具有乘法左、右单位元的环范畴是同构的。此处环是Nobasawa意义下环的简记。

In this paper we study the conditions under which Γ- rings (further subrings) have strong unity. The main results are as follows:Theorem 2 A Γ- ring M has strong unity ea(?)u∈ Mau for all u∈eM and there exists an element c of M such that la(c)= { 0 } .Theorem Let A be a subring of Γ- ring M and u∈Aau for all u∈ A. If one of the following conditions holds, then A has strong left unity:1). M satisfies the maximun condition for a right annihilators.,2). M is left Arinian;3). M is left Goldie ring;4). M is almost left Noetherian .Lemma Let A be a subring of one sided Noether Γ- ring M, a be some ele ment of Γ. If one of the following conditions holds, then A has strong unity.1). a∈Aaa∩aaA for all at A;2). for all a∈ A, Aaa is a- left annihilator of A and aaA is a-right annihila tor of A.