QUASI-MORPHIC RINGS
QUASI-MORPHIC RINGS
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DOI：
10.1142/s0219498807002454
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发表时间：
2007-10
影响因子：
0.8
通讯作者：
V. Camillo;W. K. Nicholson
中科院分区：
文献类型：
--
作者：
V. Camillo;W. K. Nicholson
称环R为左morphic环，如果R/Ra ∈ l（a），对每个a ∈ R，等价地如果存在B ∈ R使得Ra = l（B），l（a）= Rb.在本文中，我们只要求存在B和c，使得Ra = l（B）和l（a）= Rc，并且称R是左拟态的，如果这对R的每个元素a都发生.这类环包含正则环和左morphic环，并且证明了主左理想在这样的环中的有限交也是主的。进一步证明了若R是拟态的（左和右），则R是Bezout环且具有主左理想上的ACC当且仅当R是Artin主理想环.
A ring R is called left morphic if R/Ra ≅ l(a) for each a ∈ R, equivalently if there exists b ∈ R such that Ra = l(b) and l(a) = Rb. In this paper, we ask only that b and c exist such that Ra = l(b) and l(a) = Rc, and call R left quasi-morphic if this happens for every element a of R. This class of rings contains the regular rings and the left morphic rings, and it is shown that finite intersections of principal left ideals in such a ring are again principal. It is further proved that if R is quasi-morphic (left and right), then R is a Bezout ring and has the ACC on principal left ideals if and only if it is an artinian principal ideal ring.