$iw$-split modules
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, the notions of $iw$-split modules and $iw$-split dimension are introduced, and some equivalent characterizations of these notions are given. With the help of $iw$-split modules and $iw$-split dimensions, new characterizations of DW rings, semi-simple rings, and Dedekind domains are given. More precisely, it is shown that $R$ is a DW ring if and only if every $iw$-split module is an injective module; while $R$ is a semi-simple ring if and only if every $R$-module is an $iw$-split module; and $R$ is a Dedekind domain if and only if every factor module of an $iw$-split module is $iw$-split.
Abstract
In this paper, the notions of $iw$-split modules and $iw$-split dimension are introduced, and some equivalent characterizations of these notions are given. With the help of $iw$-split modules and $iw$-split dimensions, new characterizations of DW rings, semi-simple rings, and Dedekind domains are given. More precisely, it is shown that $R$ is a DW ring if and only if every $iw$-split module is an injective module; while $R$ is a semi-simple ring if and only if every $R$-module is an $iw$-split module; and $R$ is a Dedekind domain if and only if every factor module of an $iw$-split module is $iw$-split.
참고문헌 (7)
- F. A. A. Almahdi, "A note on w-split modules", Palest. J. Math, 10(1), pp.160~168 (2021)
- F. Wang, "w-injective modules and w-semi-hereditary rings", J. Korean Math. Soc, 51(3), pp.509~525 (2014)[DOI]
- F. Wang, "Two generalizations of projective modules and their applications", J. Pure Appl. Algebra, 219(6), pp.2099~2123 (2015)[DOI]
- F. Wang, "Foundations of Commutative Rings and Their Modules" (2016), Springer
- F. Wang, "The w-weak global dimension of commutative rings", Bull. Korean Math. Soc, 52(4), pp.1327~1338 (2015)[DOI]
- F. Wang, "A new version of a theorem of Kaplansky", Comm. Algebra, 48(8), pp.3415~3428 (2020)[DOI]
- F. Wang, "Two applications of Nagata rings and modules", J. Algebra Appl, 19(6), pp.2050115~ (2020)[DOI]