Really sorry for this question, but googling for some time did not help me. I was trying to understand the meaning of the following phrase:


*Let B be an augmented algebra over a semi-simple algebra T.*


But I am stuck already with "augmented algebra"... -- can not find a definition on the web.



What is "augmented algebra"?
An *augmented ring* is simply a triple $(A,M,\epsilon)$ with $A$ ring, $M$ a left $A$-module and $\epsilon:A\to M$ a surjection of $A$ modules. One says then that $A$ is augmented over $M$. You can find this defined in Cartan-Eilenberg, for example.


Often, $M$ is itself a ring and the map $\epsilon$ is also a ring morphism. This is probably the situation you have. 


