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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.

8 votes
1 answer
335 views

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 …
-1 votes
1 answer
225 views

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?
1 vote
0 answers
57 views

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 …
1 vote
0 answers
124 views

$\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 …
0 votes
0 answers
166 views

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 …
1 vote
0 answers
165 views

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 …