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A ring without identity: deny the hypothesis

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#abstract-algebra #ring-theory
167
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Extensions of indecomposable modules

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#abstract-algebra #ring-theory #modules #exact-sequence #direct-sum
167
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Principal ideal is equal to a unit multiplied by the principal ideal

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#abstract-algebra #ring-theory #proof-explanation #ideals
159
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Multiplicative group of the fraction field of a UFD

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#abstract-algebra #group-theory #ring-theory #unique-factorization-domains
27
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Well definedness of multiplicity of a polynomial.

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#abstract-algebra #ring-theory #factoring #irreducible-polynomials
91
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What is the inverse of X modulo $1 + X + X^2 + X^3 + X^4$?

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#ring-theory #inverse #irreducible-polynomials
647
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Ring homomorphism composition of surjective and injective map.

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#abstract-algebra #algebraic-geometry #ring-theory
207
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Proving that the Jacobson radical of a (not necessarily unital) ring is contained in the intersection of all left modular ideals.

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#ring-theory #radicals #noncommutative-algebra
100
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Determining if a set is a ring

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#abstract-algebra #ring-theory
189
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Residue fields of $\mathbb Z[X_1,...,X_n]$ are always finite ?

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#polynomials #ring-theory #commutative-algebra #field-theory #maximal-and-prime-ideals
121
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If $I$ is an ideal of a ring $R$, then for any $a\in R$, is there a difference between $(R/I)a$ and $Ra/I$?

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#ring-theory #modules
1.1k
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Non-example of UFD

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#abstract-algebra #ring-theory #examples-counterexamples #factoring
488
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Is there a clever way to find the units of the quotient ring $\mathbb{Z}_6[x]/\langle x^2+2x\rangle$?

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#abstract-algebra #polynomials #ring-theory #alternative-proof
529
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Integral Closure Flat

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#ring-theory #commutative-algebra #flatness
641
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Check if $x^4+4x^3+6x^2+2x+1$ is irreducible over $\mathbb Q[x]$

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#polynomials #ring-theory #irreducible-polynomials

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