List questions from ring-theory

110

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Cardinal number of $U(\Bbb Z / 4 \Bbb Z \times \Bbb Z/5 \Bbb Z)$ and zero divisors of $\Bbb Z / 45 \Bbb Z \times \Bbb Z / 27 \Bbb Z$

Published on 25 Mar 2026 - 19:07

109

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Why does $0_R\cdot m=0_M$ and $r\cdot 0_M=0_M$ in a module?

Published on 16 Apr 2026 - 6:30

38

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When is multiplication $A \otimes_{A \cap B} B \to R$ an isomorphism onto its image?

Published on 17 Apr 2026 - 15:29

279

Views

Prime and Maximal Ideals of $\mathbb{Z}[\sqrt{-10}]$

Published on 10 May 2026 - 18:59

89

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Show that $x^3=y^2+68$ has no integer solutions

Published on 14 Apr 2026 - 11:32

588

Views

Show that $R/I\otimes_R R/J \cong R/(I+J)$

Published on 11 Apr 2026 - 17:59

57

Views

Definition of homomorphism

Published on 25 Mar 2026 - 19:02

416

Views

Non-Noetherian 0-dimensional ring

Published on 11 Apr 2026 - 16:43

73

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Elements of a semigroup/ring that are powers of each other

Published on 26 Mar 2026 - 8:03

2.8k

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A commutative ring R is an integral domain $\iff a,b,c \in R, a \neq0, ab=ac \implies b=c$.

Published on 14 Apr 2026 - 14:18

45

Views

Can a bivariate polynomial with only algebraic coefficients have monic polynomial factors with non-algebraic coefficients?

Published on 12 Apr 2026 - 8:53

673

Views

Question about ring of prime order.

Published on 13 Apr 2026 - 14:55

231

Views

Real Nullstellensatz

Published on 10 May 2026 - 23:54

86

Views

Error in exercise using Cramer's rule in Dummit & Foote's book?

Published on 12 Apr 2026 - 19:12

355

Views

When Rees algebra is Noetherian?

Published on 15 May 2026 - 10:03

List Question

Cardinal number of $U(\Bbb Z / 4 \Bbb Z \times \Bbb Z/5 \Bbb Z)$ and zero divisors of $\Bbb Z / 45 \Bbb Z \times \Bbb Z / 27 \Bbb Z$

Why does $0_R\cdot m=0_M$ and $r\cdot 0_M=0_M$ in a module?

When is multiplication $A \otimes_{A \cap B} B \to R$ an isomorphism onto its image?

Prime and Maximal Ideals of $\mathbb{Z}[\sqrt{-10}]$

Show that $x^3=y^2+68$ has no integer solutions

Show that $R/I\otimes_R R/J \cong R/(I+J)$

Definition of homomorphism

Non-Noetherian 0-dimensional ring

Elements of a semigroup/ring that are powers of each other

A commutative ring R is an integral domain $\iff a,b,c \in R, a \neq0, ab=ac \implies b=c$.

Can a bivariate polynomial with only algebraic coefficients have monic polynomial factors with non-algebraic coefficients?

Question about ring of prime order.

Real Nullstellensatz

Error in exercise using Cramer's rule in Dummit & Foote's book?

When Rees algebra is Noetherian?

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