query: Semisimple matrix ring
positive_passages.docid: 142612
positive_passages.text: Matrix Ring of a Semisimple Ring
negative_passages.docid: 152457
negative_passages.text: $\mathbb Z_n$ is semisimple iff $n$ is square free
negative_passages.docid: 142863
negative_passages.text: Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
negative_passages.docid: 131843
negative_passages.text: Cartan subalgebras of a semisimple Lie algebra
negative_passages.docid: 33611
negative_passages.text: necessary and sufficient condition for trivial kernel of a matrix over a commutative ring
negative_passages.docid: 118781
negative_passages.text: product of ideals in matrix ring
negative_passages.docid: 45158
negative_passages.text: Centre of a matrix ring are $ \operatorname{diag}\{ a, a, ..., a \} $ with $ a\in Z(R) $
negative_passages.docid: 7303
negative_passages.text: How many idempotent elements does the ring ${\bf Z}_n$ contain?
negative_passages.docid: 126331
negative_passages.text: Associative ring with identity, inverses, divisors of zero and Artinianity
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 38817
negative_passages.text: Why is the ring of matrices over a field simple?
negative_passages.docid: 26661
negative_passages.text: Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
negative_passages.docid: 108975
negative_passages.text: The simple modules of upper triangular matrix algebras.
negative_passages.docid: 147157
negative_passages.text: Modules over commutative rings
negative_passages.docid: 154581
negative_passages.text: Ring of matrices isomorphic to $O := \left\{a+b\frac{1+\sqrt{D}}{2}: a, b \in \mathbb{Z} \right\}$
negative_passages.docid: 29756
negative_passages.text: Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
negative_passages.docid: 140340
negative_passages.text: Left and right R-modules