（m，n）-拟倾斜与（m，n）-几乎遗传代数
(m,n)-Quasitilted and (m,n)-Almost Hereditary Algebras
摘要：
基于对（m，n）-拟倾斜代数的研究，引入了（m，n）-几乎遗传代数.（m，n）-拟倾斜代数是由整体维数为2的拟倾斜代数通过一系列包含n-1个倾斜模和m-1个余倾斜模的（余）倾斜而得到的分段遗传代数.这类代数的整体维数为m+n，且使得任何不可分解模的投射维数至多为m，否则内射维数至多为n。我们把这两类代数联系起来，其中（m，1）-几乎遗传代数起着特殊的作用。对于这些，我们证明了任何不可分解模都位于模范畴的右部，否则就位于左部的m-模拟中。这是基于更一般的研究代数的模范畴承认一个挠自由的子范畴，使任何不可分解模在于该子范畴，否则有内射维数最多n。
英文摘要：
Motivated by the study of (m,n)-quasitilted algebras, which are the piecewise hereditary algebras obtained from quasitilted algebras of global dimension two by a sequence of (co)tiltings involving n-1 tilting modules and m-1 cotilting modules, we introduce (m,n)-almost hereditary algebras. These are the algebras with global dimension m+n and such that any indecomposable module has projective dimension at most m, or else injective dimension at most n. We relate these two classes of algebras, among which (m,1)-almost hereditary ones play a special role. For these, we prove that any indecomposable module lies in the right part of the module category, or else in an m-analog of the left part. This is based on the more general study of algebras the module categories of which admit a torsion-free subcategory such that any indecomposable module lies in that subcategory, or else has injective dimension at most n.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
