1. Matrix rings with summand intersection property
- Creator:
- Karabacak, F. and Tercan, Adnan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- modules, Summand Intersection Property, and Morita invariant
- Language:
- English
- Description:
- A ring $R$ has right SIP (SSP) if the intersection (sum) of two direct summands of $R$ is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of $R$ by $M$ has SIP if and only if $R$ has SIP and $(1-e)Me=0$ for every idempotent $e$ in $R$. Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public