theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring...

resultant ideal consists of all those polynomials whose constant coefficient is even. In any ring R, a maximal ideal is an ideal M that is maximal in the...

different types of factor rings. Maximal ideal: A proper ideal I is called a maximal ideal if there exists no other proper ideal J with I a proper subset of...

prime ideal and maximal ideal coincide, as do the terms prime filter and maximal filter. There is another interesting notion of maximality of ideals: Consider...

following equivalent properties: R has a unique maximal left ideal. R has a unique maximal right ideal. 1 ≠ 0 and the sum of any two non-units in R is...

appropriate notions of ideals, for example, rings and prime ideals (of ring theory), or distributive lattices and maximal ideals (of order theory). This...

inverse in D, and they form an ideal M. This ideal is maximal among the (totally ordered) ideals of D. Since M is a maximal ideal, the quotient ring D/M is...

R} is a commutative ring and m {\displaystyle {\mathfrak {m}}} is a maximal ideal, then the residue field is the quotient ring k {\displaystyle k} = R...

abstract algebra that in a ring with identity every proper ideal is contained in a maximal ideal and that every field has an algebraic closure. Zorn's lemma...

discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an integral domain R that...