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Results tagged with ra.rings-and-algebras
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user 24260
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Annihilators in finite rings
Let $R$ be a finite commutative ring with identity and $A$ an $R$-algebra with basis $\{1, b_1,\ldots , b_k\}$. Suppose that the center of $A$ contains the ring $R$ and there are units $u_{ij}$ in th …
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Reversible Rings
Let $A$ be a ring and $I_0\supset I_1\supset I_2\supset\ldots$ a decreasing sequence of ideals. Let $R_i=A/I_i$ be the factor ring of $A$ by the ideal $I_i.$ Let $f_i:R_{i+1}\rightarrow R_i$ be the c …
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Rings of Quaternions
This is elementary, but I have no idea how to solve it for all $s$. Actually I'm not sure if it's true. Let $\mathbb Z_{2^s}$ be the ring of integers modulo $2^s$. Considere the hamilton quaternions o …
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