Finite Dimensional $k$-Algebra has finitely many Maximal Ideals
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
95942
$k[x]/(x^n)$ module with finite free resolution is free
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
140553
An ideal which is not finitely generated
75899
Principal ideal domain with finitely many ideals
124151
Finite ring extension and number of maximal ideals
29756
Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
92822
Finite number of elements generating the unit ideal of a commutative ring
27766
Comaximal ideals in a commutative ring
77382
Left ideals of $M_n(K)$
133975
Localising a polynomial ring and non-maximal prime ideal
33642
Finite dimensional subspace of $C([0,1])$
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
104782
Polynomial irreducible - maximal ideal
79460
Atiyah-Macdonald, Exercise 8.3: Artinian iff finite k-algebra.