Structure of T-rings.(English)Zbl 0588.16021

Radical theory, Proc. 1st Conf., Eger/Hung. 1982, Colloq. Math. Soc. János Bolyai 38, 633-655 (1985).
[For the entire collection see Zbl 0575.00009.]
The authors call an associative ring R with identity a (left) T-ring if $$Ext_ R(A,B)\neq 0$$ whenever A is a non-projective left R-module and B is a non-injective one. In the case, if R is not completely reducible, there exists just one non-projective simple module N and T-rings can be divided into three types: (1) $$Soc_ N(R)\neq 0$$; (2) $$Soc_ N(R)=0$$ and Soc(R) is a left direct summand of R; (3) $$Soc_ N(R)=0$$ and Soc(R) is not a left direct summand of R. Besides some basic properties of T-rings, the authors give a full description of T-rings of type (3).
Reviewer: L.Bican

MSC:

 16Exx Homological methods in associative algebras 16S20 Centralizing and normalizing extensions 16D80 Other classes of modules and ideals in associative algebras

Zbl 0575.00009