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Is the property of Euclidean domain inherited via surjective ring homomorphism?

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#ring-theory
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Properties of $R/I$

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#ring-theory
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Prove that a ring homomorphism $f:R\to S$ is injective if $R$ is a field

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#abstract-algebra #ring-theory #self-learning
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Field extensions and algebraic/transcendental elements

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#abstract-algebra #ring-theory #field-theory
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A monomial ideal, $I =\langle xy, xz, yz\rangle$, is radical

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#ring-theory #commutative-algebra #ideals #groebner-basis #monomial-ideals
56
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Polynomial ring equals sum of sets.

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#linear-algebra #ring-theory
112
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Is the given Ring $\mathcal K(U)$ an integral domain?

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#abstract-algebra #complex-analysis #ring-theory
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Field extension of a finite field

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#abstract-algebra #ring-theory #field-theory #extension-field
302
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Let $R$ be a field. What are the $R$-submodules of $R \times R \ ?$

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#ring-theory
60
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Global Dimension 1, right annihilator

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#ring-theory #homological-algebra
46
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Ring theory question.

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#ring-theory #field-theory
297
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If $M,N$ are $R$-modules, then every submodule of $M \times N$ is the form of $U\times V,$ where $U,V$ are submodules of $M,N \ ?$

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#ring-theory
56
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Grading and commutators

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#commutative-algebra #ring-theory #noncommutative-algebra #graded-rings
3.5k
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Are integers mod n a unique factorization domain?

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#abstract-algebra #ring-theory #modular-arithmetic
1k
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Finite field with algebraic element over $\mathbb{Z}_p$

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#abstract-algebra #ring-theory #finite-fields

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