Every ideal in a Euclidean Domain is principal Post published:May 20, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingEvery ideal in a Euclidean Domain is principal

The set of natural numbers are well-ordered Post published:May 16, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingThe set of natural numbers are well-ordered

Every prime ideal is a maximal ideal in a Boolean ring Post published:May 12, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingEvery prime ideal is a maximal ideal in a Boolean ring

The only boolean ring that is an integral domain is Z/2Z Post published:May 8, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingThe only boolean ring that is an integral domain is Z/2Z

Prove that every finitely generated ideal in a Boolean ring is principal Post published:April 6, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingProve that every finitely generated ideal in a Boolean ring is principal

Show that (x) is a prime ideal of R[X] iff R is an integral ideal Post published:April 2, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingShow that (x) is a prime ideal of R[X] iff R is an integral ideal

The ideal P is a prime ideal of a commutative ring R iff R/P is an integral domain Post published:March 29, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingThe ideal P is a prime ideal of a commutative ring R iff R/P is an integral domain

The commutative ring R is a field iff the zero ideal is the maximal ideal of R Post published:March 25, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingThe commutative ring R is a field iff the zero ideal is the maximal ideal of R

The ideal M of R is maximal iff the quotient ring R/M is a field Post published:March 21, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingThe ideal M of R is maximal iff the quotient ring R/M is a field

The commutative ring R is a field iff its only ideals are 0 and R Post published:March 17, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingThe commutative ring R is a field iff its only ideals are 0 and R