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For a fixed semi-Wakamatsu-tilting module $_{A}T$, we generalize the concepts of Auslander class, Bass class, and investigate many homological properties of such classes. Moreover, we establish an equivalence between the class of $\infty$-$T$-cotorsionfree modules and a subclass of the class of $T$-adstatic modules. Finally, a similar version of Auslander-Bridger approximation theorem and a nice property of relative cotranspose are obtained.
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참고문헌 (19)
참고문헌 신청
I. Assem / 2006 / Elements of the representation theory of as-sociative algebras. Vol. 1 / Cambridge University Press
Maurice Auslander / 1991 / Applications of contravariantly finite subcategories / Advances in Mathematics 86(1):111~152
M Auslander / 1980 / Preprojective modules over artin algebras / Journal of Algebra 66(1):61~122
Silvana Bazzoni / 2010 / Equivalences induced by infinitely generated tilting modules / Proceedings of the American Mathematical Society 138(02):533~544
Silvana Bazzoni / 2011 / Derived equivalence induced by infinitely generated $n$-tilting modules / Proceedings of the American Mathematical Society 139(12):4225~4234
Maurice Auslander / 1991 / Applications of contravariantly finite subcategories / Advances in Mathematics 86(1):111~152
M Auslander / 1980 / Preprojective modules over artin algebras / Journal of Algebra 66(1):61~122
Silvana Bazzoni / 2010 / Equivalences induced by infinitely generated tilting modules / Proceedings of the American Mathematical Society 138(02):533~544
Silvana Bazzoni / 2011 / Derived equivalence induced by infinitely generated $n$-tilting modules / Proceedings of the American Mathematical Society 139(12):4225~4234
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