Projectivity of acts and morita equivalence of monoids
Projectivity of acts and morita equivalence of monoids
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行为的射影性和幺半群的森田等价
DOI：
10.1007/bf02572973
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发表时间：
1971
期刊：
影响因子：
0.7
通讯作者：
U. Knauer
中科院分区：
文献类型：
--
作者：
U. Knauer
本文将考虑a -模的非加性范畴，即取一个作用于从左出发的集合上的单形a而不是环a。这些对象被称为a -act。我们研究了不可分解的a -行为和产生子，并对这一类中的投影进行了表征。对于给定的单群a，我们描述所有的单群B，使得B行为的范畴等价于a行为的范畴。特别地，我们发现当A是群、有限或可交换时，这些范畴的等价产生了模群A和模群B之间的同构。这与加性的情况不同，在加性的情况下，交换域及其nxn矩阵环上的模的范畴是等价的。最后给出了非同构单群A和B的例子，使得相应的范畴是等价的。
In this paper we shall consider a non-additive category of A-modules, that is, instead of a ring A we take a monoid A which acts on sets from the left. These objects will be called A-acts. We investigate indecomposable A-acts and generators and characterize projectives in this category. For a given monoid A we describe all monoids B such that the category of B-acts is equivalent to the category of A-acts. In particular we find that equivalence of these categories yields an isomorphism between the monoids A and B if A is a group or finite or commutative. This differs from the additive case where the categories of modules over a commutative field and its ring of nxn matrices are equivalent. Finally we give examples of non-isomorphic monoids A and B such that the corresponding categories are equivalent.