A note on lifting isomorphisms of modules over PIDs
نویسنده
چکیده
This note has been written to supplement Keith Conrad’s [1], though it is largely independent of the latter. I am going to show some (rather elementary) properties of free modules over PIDs and apply them to drop the “full submodule” resp. “nonzero determinant” restraints which qualify many statements made in [1]. Thanks are due to Keith Conrad for a correction and helpful remarks. The LaTeX sourcecode of this note contains additional details of proofs inside “verlong” environments (i. e., between “\begin{verlong}” and “\end{verlong}”). I doubt they are of any use.
منابع مشابه
LIFTING MODULES WITH RESPECT TO A PRERADICAL
Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and$Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two$tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplusN_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting moduleis $tau_M$-lifting.
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تاریخ انتشار 2013