Almost M-projectives and nakayama rings☆
Almost M-projectives and nakayama rings☆
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几乎是M-射影和中山环☆
DOI：
10.1016/0021-8693(89)90229-9
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
Anri Tozaki
中科院分区：
文献类型：
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作者：
M. Harada;Anri Tozaki
1960年，H.Bass[3]定义了半完全环的概念，1963年E.Mares[11]将其推广到半完全模的概念。从那时起，人们考虑了各种进一步的概括。特别是，K.Oshio[161]研究了关于直和的几个重要条件下的拟半完全模。本文与他的论文以及Mueller等人的文献[12,151]密切相关，并与直接分解为空模的模上的条件(D，)(文[16]中的(C，))密切相关。这实际上是由定理[16，定理3.51]所激发的，即每个准半完美模都有上述类型的分解。在第二节中，我们将阐明直接分解为空模的模上的M-投射与条件(D，)之间的关系，条件对CL是对偶的。5、定理81。为了将(D，)翻译成同态，我们将引入几乎A4-投射的新概念，找出几乎M-投射与一个较弱条件(D‘，)之间的一些关系。在第三节准备了几个基本结果之后，在第四节，我们将把自己限制在半完全环上，并利用几乎M-投射的概念给出了具有特殊性质的右Nakayama环的一系列刻画。最后，我们将在第5节中对局部Dedekind域上具有(D，)的模进行分类。
In 1960, H. Bass [3] defined the notion of semi-perfect rings and, in 1963, E. Mares [ll] generalized it to that of semi-perfect modules. Since that time various kinds of further generalizations have been considered. In particular, K. Oshiro [161 studied quasi-semiperfect modules in connection with several important conditions on direct summands. The present paper is closely related to his paper as well as to the papers [12, 151 by Mueller and others and is cncerned with the condition (D,)(which is (C,) in [16]) over modules with direct decomposition into hollow modules. This is indeed motivated by the theorem [16, Theorem 3.51 that every quasisemiperfect module has the above type of decomposition. In Section 2 we shall clarify relationships between M-projectives over modules with direct decomposition into hollow modules and the condition (D,), which is dual to Cl. 5, Theorem 81. In order to translate (D,) in terms of homomorphisms, we shall introduce a new concept of almost A4-projectives to find some relations between almost M-projectives and a weaker condition (D’,). After preparing several basic results in Section 3, we shall, in Section 4, restrict ourselves to semi-perfect rings and give a series of characterizations of right Nakayama rings with special properties by making use of the concept of almost M-projectives. Finally, we shall classify modules with (D,) over a local Dedekind domain in Section 5.