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Results tagged with ra.rings-and-algebras
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user 19077
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.
24
votes
Example for column rank $\neq$ row rank
I will only consider matrices over division rings, since defining rank over more general rings, in particular those with zero divisors, involves difficulties rather independent of those posed by non-c …
- 1,683
6
votes
Expressing $-\operatorname{adj}(A)$ as a polynomial in $A$?
This formula can be obtained during a proof of the Cayley-Hamilton theorem, as is indicated on its Wikipedia article. The essence of the argument is that Euclidean division by a monic polynomial (on t …
- 1,683