rschwieb
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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