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Results tagged with ra.rings-and-algebras
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user 15488
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.
3
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Skew fraction fields of *-algebras
Let $R$ be a (non-commutative) domain satisfying the (right) Ore condition; i.e. for all $a,b\in R$ one can find $\beta_1,\beta_2\in R$ such that $a\beta_1=b\beta_2$. In the well known construction of …
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6
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2
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537
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Positive matrices matrices over commutative rings
Assume that $R$ is a commutative ring with a ring compatible ordering and let $A$ and $B$ be symmetric $n\times n$ matrices with entries in $R$ such that $\sum x_iA_{ij}x_j\geq 0$ and $\sum x_iB_{ij}x …
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6
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3
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Trace of the identity map in a projective module
Let $A$ be a commutative algebra (over the complex numbers, with a unit) and let $M$ be a finitely generated projective $A$-module, and let $m_1,\ldots,m_n$ be a set of generators of $M$. The Dual Bas …
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7
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answer
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Equivalence of idempotents and projective modules over nonunital rings
For a nonunital ring $R$ (or "rng") one has to be a little bit careful when considering the category of (left or right) $R$-module and, furthermore, the standard equivalent definitions of projective m …
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2
votes
1
answer
931
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When are two projective modules of equal rank isomorphic?
Let $R$ be a commutative ring and let $M,N$ be two finitely generated projective $R$-modules which have equal rank (not necessarily constant). What kind of general results are there concerning the que …
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9
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Which concept of dimension of a ring of functions on a manifold, gives the dimension of the ...
Let $R$ be a ring of (smooth?) functions on a (connected?) manifold of dimension $n$. What concept of dimension (of the ring $R$) gives the dimension of the manifold? To what class of rings does this …
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7
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0
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How to prove that a projective module is not free?
Let $A$ be a noncommutative (perhaps $\ast$-) algebra (over $\mathbb{C}$) and let $M$ be a projective module defined via a projector $P\in M_n(A)$; i.e. $M=P(A^n)$. Furthermore, assume that all object …
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