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. Download MestREC Crack with Keygen and Serial Number Version 3.07 (Updated). The latest version. crack or serial number Keygen. We have the largest crack, keygen and serial number data base.Q:

$K$-theory of two rings with idempotent ring homomorphism

Let $R$ and $S$ be commutative rings such that $R$ and $S$ have unit elements. Let $\phi: R \to S$ be a ring homomorphism such that $\phi(1) = 1$.
Question: Does it follow that $K(R) \cong K(S)$?

A:

Here are a few hints. Since $S$ is commutative, its $K$-theory is just the $K$-theory of $S$, so it suffices to prove that $R$ is a product of matrix rings over $S$. Can you find a basis for $R$ that satisfies certain criteria?

. G. Stüttgenbach, *Tensor products of module categories*, Comm. Algebra 31 (4) (2003) 1277-1306.

S. Bazzoni, T. Brüstle, and P. Solberg, *On the stable components of Nakayama algebras*, Homology Homotopy Appl. 15 (3) (2013) 513-535.

H. Bischby, *Higman’s criterion and the second cohomology group of a group*, J. London Math. Soc. 9 (1974) 693-698.

H. Bischby, *Finite dimensional Lie subalgebras of polynomial rings and the Golod-Shafarevich property*, Trans. Amer. Math. Soc. 250 (1979) 121-136.

H. Bischby, *A Golod-Shafarevich result*, Manuscripta Math. 41 (1983) 1-11.

T. Brüstle, J. Smith, *The homology of almost-flat $A_\infty$-algebras*, J. Topol. Anal. 2 (3) (2010) 257-272.

M. Cohen, *Infinite-dimensional Lie algebras in a non-Noetherian ring*, Canadian J. Math

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