A decomposition theorem for Utumi and dual-Utumi modules
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We show that if $M$ is a Utumi module, in particular if $M$ is quasi-continuous, then $M =Q \oplus K$, where $Q$ is quasi-injective that is both a square-full as well as a dual-square-full module, $K$ is a square-free module, and $Q$ \& $K$ are orthogonal. Dually, we also show that if $M$ is a dual-Utumi module whose local summands are summands, in particular if $M$ is quasi-discrete, then $M =P \oplus K$ where $P$ is quasi-projective that is both a square-full as well as a dual-square-full module, $K$ is a dual-square-free module, and $P$ \& $K$ are factor-orthogonal.
Abstract
We show that if $M$ is a Utumi module, in particular if $M$ is quasi-continuous, then $M =Q \oplus K$, where $Q$ is quasi-injective that is both a square-full as well as a dual-square-full module, $K$ is a square-free module, and $Q$ \& $K$ are orthogonal. Dually, we also show that if $M$ is a dual-Utumi module whose local summands are summands, in particular if $M$ is quasi-discrete, then $M =P \oplus K$ where $P$ is quasi-projective that is both a square-full as well as a dual-square-full module, $K$ is a dual-square-free module, and $P$ \& $K$ are factor-orthogonal.
참고문헌 (9)
- Nanqing Ding, "D4-Modules", Journal of Algebra and Its Applications, 16(09), pp.1750166~ (2017), World Scientific Pub Co Pte Lt[DOI]
- Yasser Ibrahim, "Dual-square-free modules", Communications in Algebra, 47(7), pp.2954~2966 (2019), Informa UK Limited[DOI]
- Yasser Ibrahim, "Utumi modules", Communications in Algebra, 46(2), pp.870~886 (2018), Informa UK Limited[DOI]
- Yasser Ibrahim, "Dual Utumi modules", Communications in Algebra, 47(9), pp.3889~3904 (2019), Informa UK Limited[DOI]
- Isao Kikumasa, "OnH-supplemented modules over a right perfect ring", Communications in Algebra, 46(5), pp.2063~2072 (2018), Informa UK Limited[DOI]
- Isao Kikumasa, "Factor square full modules", Communications in Algebra, 49(6), pp.2326~2336 (2021), Informa UK Limited[DOI]
- Derya Keskin Tütüncü, "On dual of square free modules", Communications in Algebra, 46(8), pp.3365~3376 (2018), Informa UK Limited[DOI]
- S. H. Mohamed, "Continuous and discrete modules" (1990), Cambridge University Press
- R. Wisbauer, "Foundations of module and ring theory" (1991), Gordon and Breach Science Publishers