Silting modules and ring epimorphisms
Silting modules and ring epimorphisms
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DOI：
10.1016/j.aim.2016.08.035
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发表时间：
2015-04
期刊：
影响因子：
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通讯作者：
Lidia Angeleri Hugel;F. Marks;Jorge Vit'oria
中科院分区：
文献类型：
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作者：
Lidia Angeleri Hugel;F. Marks;Jorge Vit'oria
存在与环满态和倾斜模相关的公知构造。淤积模块的新概念为研究这种相互作用提供了一个更广泛的框架。每一个部分淤泥模块，我们关联一个环满射，我们明确描述为一个幂等商的自同态环的Bongartz完成。对于遗传环，这个赋值被用来通过填充模来参数化同调环满态。进一步证明了在有限维代数的情况下，遗传环的同调环满射构成一个格，它完成了非交叉划分的偏序集。
There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism which we describe explicitly as an idempotent quotient of the endomorphism ring of the Bongartz completion. For hereditary rings, this assignment is used to parametrise homological ring epimorphisms by silting modules. We further show that homological ring epimorphisms of a hereditary ring form a lattice which completes the poset of noncrossing partitions in the case of finite dimensional algebras.