Why the Jacobson radical of a finite generated Z-algebra is 0
57123
Jacobson radical of a finitely generated $\mathbb Z$-algebra is nilpotent
68807
How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)
37960
Zero Divisors in Direct Product of Rings
140938
Finitely generated projective module
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
18066
Prove that any non-zero-divisor of a finite dimensional algebra has an inverse
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
16727
Intersection of finitely generated ideals
44065
If $B$ is finitely generated as a $k$-algebra, and $\phi:A\to B$ is a $k$-algebra map, is $\phi^{-1}(M)$ maximal for any maximal $M\subset B$?
31585
Primary ideals of $\mathbb{Z}$
69398
Rank-nullity theorem for free $\mathbb Z$-modules
134726
Show the polynomial is irreducible in $\textbf Z_2$
29635
Fields finitely generated as $\mathbb Z$-algebras are finite?
80879
Can a quotient field ever be finitely generated as an algebra?
41895
Show $\text{Hom}_{Ab}(A,\mathbb{Q}) = \{0\}$ for finite $A$