List questions from ring-theory

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Peirce decomposition of a ring: must the ideal generators be idempotent in characteristic 2?

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Direct sums of left ideals and orthogonal idempotents

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285

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Cartesian product of fields is semisimple iff the index set is finite

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28

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Ideal generated in a noetherian ring

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Extending a ring hom from $R \to L$ to $K \to L$, where $K$ is fraction field of domain $R$.

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Matrix Ring of semisimple algebra over $\mathbb{C}$

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105

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Do products exist in CRing

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How do we compute the rational cohomology ring $H^*\left(\bigsqcup_{i\ge 1}S^n;\mathbb{Q}\right)$?

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Prove that the image of an ideal under a ring homomorphism $\mathbb Z[x]/I\to M_2(\mathbb Z)$ is not an ideal

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Integral domain.

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Semisimple subalgebras of $M_4(\mathbb{C})$

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Definition of socle of a module

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How to prove a specific quotient of polynomial ring is a free module?

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About Semigroup & Semiring homomorphism

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List Question

Nilpotent Jacobson radical

Peirce decomposition of a ring: must the ideal generators be idempotent in characteristic 2?

Direct sums of left ideals and orthogonal idempotents

Cartesian product of fields is semisimple iff the index set is finite

Ideal generated in a noetherian ring

Extending a ring hom from $R \to L$ to $K \to L$, where $K$ is fraction field of domain $R$.

Matrix Ring of semisimple algebra over $\mathbb{C}$

Do products exist in CRing

How do we compute the rational cohomology ring $H^*\left(\bigsqcup_{i\ge 1}S^n;\mathbb{Q}\right)$?

Prove that the image of an ideal under a ring homomorphism $\mathbb Z[x]/I\to M_2(\mathbb Z)$ is not an ideal

Integral domain.

Semisimple subalgebras of $M_4(\mathbb{C})$

Definition of socle of a module

How to prove a specific quotient of polynomial ring is a free module?

About Semigroup & Semiring homomorphism

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