List questions from ring-theory

Published on 17 Apr 2026 - 2:07

113

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Prove $M$ is a maximal ideal of $R$ and $\frac{R}{M}$ is a field having 25 elements

Published on 16 Apr 2026 - 3:34

286

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Prove that a ring with 48 elements is not an integral domain

Published on 25 Mar 2026 - 20:34

138

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For $x+y \in \mathbb{Q}[x,y]$, show that $\langle x+y\rangle$ is maximal among all principal ideals and show that it is not maximal among all ideals

Published on 16 Apr 2026 - 9:15

144

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Classification of primary ideals of $\mathbb{Z}[X]/(X^2+d)$

Published on 16 Apr 2026 - 8:44

270

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Fully-faithful functors between categories of modules

Published on 02 May 2026 - 13:13

195

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Composition Factors of a Quotient Module

Published on 10 Apr 2026 - 19:32

29

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Matrix representation of $R^0\rightarrow R^m$

Published on 17 Apr 2026 - 10:06

367

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Is F[x] isomorphic to Z for any field F?

Published on 24 Apr 2026 - 6:51

425

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Number of invertible elements in quotient ring

Published on 01 Apr 2026 - 2:06

288

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Surjective Ring Homomorphism from Center to Center

Published on 25 Mar 2026 - 14:31

296

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References on ring congruences and correspondence with ideals

Published on 16 Apr 2026 - 17:21

122

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Polynomial division in the ring $R=\mathbb{Z}_5[x]/\langle x^3+x^2+x+3\rangle.$

Published on 20 Apr 2026 - 15:04

52

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Prove the relation $\sim$ on $M\times T$ is an equivalence relation.

Published on 16 Apr 2026 - 14:39

355

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Zero polynomials, null polynomials and characteristic 2.

Published on 16 Apr 2026 - 9:03

List Question

Two different maximal ideals of a commutative ring

Prove $M$ is a maximal ideal of $R$ and $\frac{R}{M}$ is a field having 25 elements

Prove that a ring with 48 elements is not an integral domain

For $x+y \in \mathbb{Q}[x,y]$, show that $\langle x+y\rangle$ is maximal among all principal ideals and show that it is not maximal among all ideals

Classification of primary ideals of $\mathbb{Z}[X]/(X^2+d)$

Fully-faithful functors between categories of modules

Composition Factors of a Quotient Module

Matrix representation of $R^0\rightarrow R^m$

Is F[x] isomorphic to Z for any field F?

Number of invertible elements in quotient ring

Surjective Ring Homomorphism from Center to Center

References on ring congruences and correspondence with ideals

Polynomial division in the ring $R=\mathbb{Z}_5[x]/\langle x^3+x^2+x+3\rangle.$

Prove the relation $\sim$ on $M\times T$ is an equivalence relation.

Zero polynomials, null polynomials and characteristic 2.

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