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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.

0 votes
1 answer
208 views

I need to prove that any element in a rings is representable as a product of some element an...

Let $R$ be an associative ring with identity and let $x$ be an arbitrary element from the ring $R$. Could you please help me to prove that $x=ye$, where $y$ is some element in $R$ and $e$ is some prim …
ingrem's user avatar
  • 23
1 vote
1 answer
425 views

Another question about primitive central idempotents in associative unital rings (yes, again!)

Let $R$ be an arbitrary associative unital ring and let $x \in R$. Can we always represent $x$ as a finite or infinite sum $x=\sum_{i}y_ie_i$ where $y_i\in R$ and each $e_i$ is a primitive central ide …
ingrem's user avatar
  • 23