Intersection9

The set of prime ideals of a commutative ring contains inclusion-minimal elements
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.36 Solution:...
Some more properties of ideal arithmetic
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.35 Solution:...
The set of ideals of a ring is closed under arbitrary intersections
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.18 Solution:...
The intersection by an abelian normal subgroup is normal in the product
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.20 Let $G$ b...
Bounds on the index of an intersection of two subgroups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.10 Let $G$ b...
Finite subgroups with relatively prime orders intersect trivially
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.8 Let $G$ be...
The intersection of a nonempty collection of subrings is a subring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.4 Prove that...
Basic properties of normalizers with respect to a subgroup
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.2 Exercise 2.2.9 Let $G$ be...
An arbitrary intersection of subgroups is a subgroup
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.10 Let $G$ b...