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Apr
14
comment Each element is invertible
@MaryStar that would imply $baR=\{0\}$
Apr
14
comment Each element is invertible
@MaryStar yes, it is just set equality
Apr
14
comment Each element is invertible
No, just that $(1-ba)R=\{0\}$
Apr
14
answered $\mathbb{Z}_p \hookrightarrow R$ is it necessary $R$ commutative?
Apr
14
answered The properties of a group with such operator
Apr
14
answered Why do division algebras always have a number of dimensions which is a power of $2$?
Apr
14
comment Show that there are finitely many different principal ideals
The linked duplicate was in the related list on the right, and I believe it was probably in the list you saw as you titled the question. Please pay attention to those.
Apr
12
comment If every polynomial in $F[x]$ splits then there exists no nontrivial algebraic extension
Said another way, "algebraic extension" means every element is algebraic, (in particular $\alpha$.) Trancendental means "not algebraic."
Apr
11
comment Show that $I$ is an ideal
@MaryStar $A\oplus B =R$ means $A+B=R$ and $A\cap B=\{0\}$.
Apr
11
comment What algebra do you get if you switch the sign of one pair of anticommuting quaternion products?
@RobWallace Often, the origin of a construction can hold valuable clues as to whether or not it may have certain properties. How did you come about this algebra?
Apr
11
answered Prove or disprove that $U+W=V$ for a set of given conditions.
Apr
11
answered Each element is invertible
Apr
11
comment Show that $I$ is an ideal
@MaryStar There might be another way, but it seems like this is the simplest path. An element $e$ is called idempotent if $e^2=e$.
Apr
10
comment Show that $I$ is an ideal
@MaryStar if you know what an idempotent element is then I should not have to explain why $ir$ is idempotent. If you ask a more specific question about the last paragraph I may respond.
Apr
10
answered Show that $I$ is an ideal
Apr
8
comment How do I find the ideals in the ring $\mathbb F_3[x]/(x^2+2)$?
The same way you do in any polynomial ring over a field: you find the divisors of $x^2+2$.
Apr
8
answered Multiplicative identity in a monoid ring.
Apr
8
answered Show $v\in FS_n$ is an $F$-multiple.
Apr
8
answered Show that if v $\in$ V is an eigenvector of T, then [v] $\in$ P(V) is a fixed point of the projective transformation $\tau$ defined by T.
Apr
8
answered Monoid with two binary operations