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Results tagged with ra.rings-and-algebras
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user 80790
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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Can we classify all commutative unital algebras over the reals that are closed under $\sqrt{}$?
Can we classify all finite dimensional commutative (but not necessarily associative) unital algebras over the reals in which every element is a square?
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Nonassociative algebras closed under $\sqrt{\ }$?
Consider a non-associative commutative unital algebra of finite dimension where the product is defined by a Cayley table such that elements are generated with real number coefficients
$(a_0, \dotsc, a …
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Density of extended Mersenne numbers?
Consider the subset of odd positive integers defined and constructed as follows by these rules :
A) $1$ is in the set.
B) if $x$ is in the set , then $2x + 1$ is in the set.
C) if $x$ and $y$ are in t …
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166
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When does this commutative non-associative algebra have nilpotent elements?
Consider a non-associative commutative unital algebra of finite dimension where the product is defined by a Cayley table such that elements are generated with real number coefficients
$(a_0, \dotsc, a …
- 769
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0
answers
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$\sin(\frac{\pi}{p}) $ not expressible by positive radicals and $\sin(\frac{\pi}{q_i})$?
We have the following identities:
$\sin(\frac{\pi}{1})=0$
$\sin(\frac{\pi}{2})=1$
$\sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}$
$\sin(\frac{\pi}{4})=\sqrt{\frac{1}{2}}$
Lets start with a definition.
Rules …
- 769
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About nilpotent Jordan algebras, matrix representations and formally real algebras
Given an non-commutative associative unital algebra A of characteristic $0$, one can construct a Jordan algebra $A+$ using the same underlying addition vector space.
Notice first that an associative a …
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