Domino
Feb26-11, 07:08 AM
I stuck with this algebra question.
I try to prove that the exterior algebra R ove r k^d
the k-algebra that generated by x_1,...x_d and x_ix_j = - x_jx_i for each i,j , has just one simple module which is not faithful.
I think the only simple module is k but I not really sure if my idea does work or not
Can I use the fact {x^2}_i = 0 for all i, then k has cyclic subrings.If yes, then HOW?
Also, one more question if k is finitely generated, is that enough to say that R is Artinian?
Thank you
I try to prove that the exterior algebra R ove r k^d
the k-algebra that generated by x_1,...x_d and x_ix_j = - x_jx_i for each i,j , has just one simple module which is not faithful.
I think the only simple module is k but I not really sure if my idea does work or not
Can I use the fact {x^2}_i = 0 for all i, then k has cyclic subrings.If yes, then HOW?
Also, one more question if k is finitely generated, is that enough to say that R is Artinian?
Thank you