Integral elements form a ring. What can we say about polynomials of sum and product?
48977
Polynomials having as roots the sum (respectively, the product) of two algebraic elements
84149
Prove that an infinite ring with finite quotient rings is an integral domain
85961
Is the ring and semi-ring definition of algebra and set linked?
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
41629
Structure of ideals in the product of two rings
117590
Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal
108775
Identify the ring $\mathbb {Z}[i]/(2 + i) $
87946
Proving that the unities of a ring form a group under multiplication
13174
Show that $A[X]/(aX+b)$ is an integral domain
122104
Ideal products and calculating with ideals
51428
Do these two observations suffice to show that a finite boolean ring must be of the form $\mathbb{Z}_2\times\cdots\times\mathbb{Z}_2$?
92420
Characteristic of  a Non-unital Integral Ring
10254
Is the Polynomial Factor Theorem true over all commutative rings?
32772
Proving units in a ring
111824
Sum of nilpotent and element is a unit in ring?
111104
Ring theory notation question
57031
Ring of fractions of $R$ is integral over $R$