지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
오류제보하기
For an ideal L of a preadditive category A, we study whenthe canonical functor C: A → A/L is local. We prove that there existsa largest full subcategory C of A for which the canonical functor C : C → C/L is local. Under this condition, the functor C turns out to bea weak equivalence between C and C/L. If A is additive (with splittingidempotents), then C is additive (with splitting idempotents). The category C is ample in several cases, such as the case when A = Mod-R andI is the ideal Δ of all morphisms with essential kernel. In this case, thecategory C contains, for instance, the full subcategory F of Mod-R whoseobjects are all the continuous modules. The advantage in passing fromthe category F to the category F/L lies in the fact that, although thetwo categories F and F/L are weakly equivalent, every endomorphismhas a kernel and a cokernel in F/Δ, which is not true in F. In the finalsection, we extend our theory from the case of one ideal I to the case ofn ideals L1, . . . , Ln.
목차
등록된 정보가 없습니다.
참고문헌 (11)
참고문헌 신청
A. Alahmadi / 2009 / A note on almost injective modules / Math. J. Okayama Univ 51 : 101 ~ 109
A. Facchini / 1998 / Module Theory, Endomorphism rings and direct sum decompositions in some classes of modules / Birkh¨auser Verlag
A. Facchini / 2006 / A characterization of additive categories with the Krull-Schmidt property, Algebra and its applications / Contemp. Math. 419 : 125 ~ 129
A. Facchini / 2007 / Representations of additive categories and direct-sum decompositions of objects / Indiana Univ. Math. J 56 (2) : 659 ~ 680
A. Facchini / 2011 / Endomorphism rings with finitely many maximal right ideals / Comm. Algebra 39 (9) : 3317 ~ 3338
A. Facchini / 1998 / Module Theory, Endomorphism rings and direct sum decompositions in some classes of modules / Birkh¨auser Verlag
A. Facchini / 2006 / A characterization of additive categories with the Krull-Schmidt property, Algebra and its applications / Contemp. Math. 419 : 125 ~ 129
A. Facchini / 2007 / Representations of additive categories and direct-sum decompositions of objects / Indiana Univ. Math. J 56 (2) : 659 ~ 680
A. Facchini / 2011 / Endomorphism rings with finitely many maximal right ideals / Comm. Algebra 39 (9) : 3317 ~ 3338
이 논문의 저자 정보
최근 본 자료
댓글(0)
0