论文标题
莫里塔环上的合并对和模型结构
Cotorsion pairs and model structures on Morita rings
论文作者
论文摘要
本文是在某些Morita戒指上研究Cotorsion对和Abelian模型结构\ $λ= \ left（\ begin {smallmatrix} a＆{} _an_b {} _bm_a＆b \ end {smallmatrix} \ right）$。从CotorSion Pairs $（\ Mathcal U，\ Mathcal X）$和$（\ Mathcal V，\ Mathcal Y）$，分别以$ a $ a-mod和$ b $ -mod为单位，一个人以$λ$ -mod构建4种CotorSion对。甚至存在一个代数$λ$，因此上面的四个Cotorsion对成对不同。研究了这些cotorsion对的遗传和完整性。识别问题，即，当前两个结转对相同时，当研究第二个cotorsion对时，研究了。通过明确给出相应的Hovey Triples和Quillen的同型类别，获得了$λ$ \ mbox { - } {\ rm mod}上的各种模型结构。特别是，由兼容的广义投射（分别是注射式）的cotorsion对诱导的吉莱斯皮霍夫三元组和吉莱斯皮·霍夫三元组是明确制作的。
This paper is to study cotorsion pairs and abelian model structures on some Morita rings \ $Λ=\left(\begin{smallmatrix} A & {}_AN_B {}_BM_A & B\end{smallmatrix}\right)$. From cotorsion pairs $(\mathcal U, \mathcal X)$ and $(\mathcal V, \mathcal Y)$, respectively in $A$-Mod and $B$-Mod, one constructs 4 kinds of cotorsion pairs in $Λ$-Mod. There even exists an algebra $Λ$ such that the four cotorsion pairs above are pairwise different. The heredity and completeness of these cotorsion pairs are studied. The problem of identifications, namely, when the first two cotorsion pairs are the same, and when the second two cotorsion pairs are the same, is investigated. Various model structures on $Λ$\mbox{-}{\rm Mod} are obtained, by explicitly giving the corresponding Hovey triples and Quillen's homotopy categories. In particular, cofibrantly generated Hovey triples, and the Gillespie-Hovey triples induced by compatible generalized projective (respectively, injective) cotorsion pairs, are explicitly contructed.
