Dimension of the vector space given by the quotient of an Artin ring by the product of all its maximal ideals
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
47086
Quotient rings and free modules
96144
Every element outside the maximal ideal of a local ring is a unit
150911
Prove that the ring is Artinian and find a composition series of ideals
105913
Calculations in quotient rings
26780
Dimension of cone of projective variety
50445
Explaining the product of two ideals
38571
Localization of a total quotient ring of a reduced ring
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
116000
Prove that prime ideals of a finite ring are maximal
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
15686
Product of a Lie ideal with a subalgebra
29019
Ideals in direct product of rings
89782
To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field
98818
Quotient ring of a localization of a ring
42871
Quotient of a local regular ring
111114
Prove that an ideal in $k[x,y]$ is a prime ideal