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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,387 - 1,400 (14page)
- DOI
- 10.4134/BKMS.b200924
이용수
초록· 키워드
오류제보하기
Suppose that $T=\left(\begin{smallmatrix} A&0\\U&B \end{smallmatrix}\right)$ is a formal triangular matrix ring, where $A$ and $B$ are rings and $U$ is a $(B, A)$-bimodule. Let $\mathfrak{C}_{1}$ and $\mathfrak{C}_{2}$ be two classes of left $A$-modules, $\mathfrak{D}_{1}$ and $\mathfrak{D}_{2}$ be two classes of left $B$-modules. We prove that $(\mathfrak{C}_{1},\mathfrak{C}_{2})$ and $(\mathfrak{D}_{1},\mathfrak{D}_{2})$ are admissible balanced pairs if and only if $(\textbf{p}(\mathfrak{C}_{1}, \mathfrak{D}_{1}), \textbf{h}(\mathfrak{C}_{2}, \mathfrak{D}_{2}))$ is an admissible balanced pair in $T$-Mod. Furthermore, we describe when $(\mathfrak{P}^{\mathfrak{C}_{1}}_{\mathfrak{D}_{1}}, \mathfrak{I}^{\mathfrak{C}_{2}}_{\mathfrak{D}_{2}})$ is an admissible balanced pair in $T$-Mod. As a consequence, we characterize when $T$ is a left virtually Gorenstein ring.
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참고문헌 (18)
참고문헌 신청
Javad Asadollahi / 2006 / On the vanishing of Ext over formal triangular matrix rings / Forum Mathematicum 18(6):951~966
M Auslander / 1980 / Preprojective modules over artin algebras / Journal of Algebra 66(1):61~122
A. Beligiannis / 2007 / Homological and homotopical aspects of torsion theories / Mem. Amer. Math. Soc 188(883):viii~207
Xiao-Wu Chen / 2010 / Homotopy equivalences induced by balanced pairs / Journal of Algebra 324(10):2718~2731
Edgar E. Enochs / 1981 / Injective and flat covers, envelopes and resolvents / Israel Journal of Mathematics 39(3):189~209
M Auslander / 1980 / Preprojective modules over artin algebras / Journal of Algebra 66(1):61~122
A. Beligiannis / 2007 / Homological and homotopical aspects of torsion theories / Mem. Amer. Math. Soc 188(883):viii~207
Xiao-Wu Chen / 2010 / Homotopy equivalences induced by balanced pairs / Journal of Algebra 324(10):2718~2731
Edgar E. Enochs / 1981 / Injective and flat covers, envelopes and resolvents / Israel Journal of Mathematics 39(3):189~209
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