If R[x] is a P.I.D. and R commutative, then R is a field Post published:June 27, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingIf R[x] is a P.I.D. and R commutative, then R is a field

A subring R of the PID R[x] is an integral domain Post published:June 23, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingA subring R of the PID R[x] is an integral domain

Any two nonzero elements of a principal ideal domain have a least common multiple Post published:June 21, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingAny two nonzero elements of a principal ideal domain have a least common multiple

Two ideals (a) and (b) in PID are comaximal iff gcd(a,b) = 1 Post published:June 19, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingTwo ideals (a) and (b) in PID are comaximal iff gcd(a,b) = 1

A quotient of a principal ideal domain by a prime is again a P.I.D. Post published:June 15, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingA quotient of a principal ideal domain by a prime is again a P.I.D.

Every nonzero prime ideal in a P.I.D. is a maximal ideal Post published:June 13, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingEvery nonzero prime ideal in a P.I.D. is a maximal ideal