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Group ring isomorphic to matrix ring

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#matrices #ring-theory #group-rings #ring-isomorphism
296
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Are the distributive and abelian properties inherited from a ring to a SUBSET of the ring?(The subset is closed under both the operations)

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#abstract-algebra #ring-theory
254
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Total ring of fractions of non-noetherian reduced ring

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#abstract-algebra #ring-theory
196
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Show that this extension is not integral.

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#ring-theory #commutative-algebra
259
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Relation between Jacobson radical of an ideal and the jacobson radical of the ring

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#abstract-algebra #ring-theory #maximal-and-prime-ideals
616
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Unit in an Integral Domain $R$ implying a polynomial is irreducible in $R[X]$

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#abstract-algebra #polynomials #ring-theory #irreducible-polynomials
535
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Commutative Ring with Identity

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#abstract-algebra #ring-theory
62
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Integral Domains And Fields

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#abstract-algebra #ring-theory #integral-domain
42
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Maximal Ideal and its relationship with the ring

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#abstract-algebra #ring-theory #maximal-and-prime-ideals
442
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$(\mathbb{R}, \oplus, \odot)$ is a field? Given $a \oplus b=a+b+1$ and $a \odot b=a+b+ab$.

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#abstract-algebra #proof-verification #ring-theory
653
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Proving a ring-homomorphism using a group-homomorphism

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#group-theory #ring-theory #group-homomorphism #ring-homomorphism
307
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$I$-torsion functor and $\sqrt{I}$

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#abstract-algebra #ring-theory #commutative-algebra #modules #local-cohomology
500
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Dummit 7.5.2. (Ring of fractions)

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#abstract-algebra #ring-theory
195
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How to prove that $\mathbb{Z}[(1+\sqrt{2})/2]$ is a Euclidean domain?

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#abstract-algebra #ring-theory #euclidean-domain
64
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Number of irreducible polynomials of degree 4 on $\boldsymbol{Z}_3[x]$.

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#ring-theory

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