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Cardinalities of bases of a free $R$ module are same?

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#ring-theory #modules
913
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Maximal ideals in $\mathbb{Z}[x]$

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#abstract-algebra #ring-theory #ideals
495
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"Primeness" of C[x] in B[x], where A is a subring of B and C is the integral closure of A in B.

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#abstract-algebra #commutative-algebra #ring-theory
486
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Showing that $R / I$ is a ring

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#abstract-algebra #ring-theory
7.1k
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Examples of Commutative Rings with $1$ that are not integral domains besides $\mathbb Z/n\mathbb Z$?

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#ring-theory
343
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Span and Smallest Submodule Proof

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#ring-theory #proof-writing #modules
55
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Definition of h.c.f./g.c.d. not fitting with $\mathbb{Z}$

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#number-theory #ring-theory
321
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Intuition? how the author reaches the answer?

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#ring-theory #commutative-algebra #groebner-basis #monomial-ideals
2.7k
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Quotient field of a localization

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#abstract-algebra #ring-theory #commutative-algebra
78
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Example of $\sum_i a_i\otimes b_i\in M\otimes_AN$ which cannot be written as $a\otimes b$

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#ring-theory #commutative-algebra #examples-counterexamples #tensor-products
1.5k
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Ideal of a polynomial ring, and an isomorphism between $R[x]/I$ and $R$

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#abstract-algebra #ring-theory
8.4k
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Show that $M_2(\mathbb{R})$ has no non-trivial two-sided ideals

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#abstract-algebra #matrices #ring-theory #ideals
359
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Proof on unital ring isomorphism

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#abstract-algebra #ring-theory
196
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Question about comaximal ideal proof

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#abstract-algebra #ring-theory #ideals
283
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What does $R^{\times}$ mean for a ring?

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#abstract-algebra #ring-theory

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