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Results tagged with ra.rings-and-algebras
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user 82143
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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Subring of ring
Let given ring $R$ without zero divizors, where adittive group of $R$ with zero torsion. Let given subring $R_0\leq R$, and $p$ is prime number, such that $\forall r\in R, \exists i>0 : p^ir\in R_0$. …
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Subring of ring
Solution to second question in particular case, when $R_0/pR_0$ without zero divisors:
Note that $R_0/pR_0$ is finite dimensional vector space, $\dim R_0/pR_0\leq rk(R_0)$. So easy to see that $R_0/p …
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Beaumont - Pierce Principal theorem
In book R. Göbel, P. Hill, Wolfgang "Abelian Group Theory and Related Topics", I found next Beaumont -Pierce Principal theorem: Any torsion-free ring $R$ of finite rank is quasi-equal to $S\oplus N$, …
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Derivations of special rings
Consider $p$-adic field $\mathbb{Q}_p$ and let $A$ be any finite dimensional $\mathbb{Q}_p$ algebra without zero divisors (and maybe without $1$). Now we can look on $A$ as on a ring $A_{\mathbb{Z}}$ …
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