Turkish Journal of Mathematics
Article Title
DOI
10.3906/mat-1609-77
Abstract
In this paper, matrix rings with the summand intersection property (SIP) and the absolute direct summand (ads) property (briefly, $SA$) are studied. A ring $R$ has the right SIP if the intersection of two direct summands of $R$ is also a direct summand. A right $R$-module $M$ has the ads property if for every decomposition $M=A\oplus B$ of $M$ and every complement $C$ of $A$ in $M$, we have $M=A\oplus C$. It is shown that the trivial extension of $R$ by $M$ has the SA if and only if $R$ has the SA, $M$ has the ads, and $(1-e)Me=0$ for each idempotent $e$ in $R$. It is also shown with an example that the SA is not a Morita invariant property.
Keywords
Ads property, summand intersection property, trivial extension
First Page
2657
Last Page
2663
Recommended Citation
MUTLU, FİGEN TAKIL
(2018)
"On matrix rings with the SIP and the Ads,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 42.
https://doi.org/10.3906/mat-1609-77
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/42
