mathematics, especially ring theory, a regular ideal can refer to multiple concepts. In operator theory, a right ideal i {\displaystyle {\mathfrak {i}}} in...

{\displaystyle y\in J} ⁠. Regular ideal: This term has multiple uses. See the article for a list. Nil ideal: An ideal is a nil ideal if each of its elements...

Neumann regular element if there exists an x such that a = axa. An ideal i {\displaystyle {\mathfrak {i}}} is called a (von Neumann) regular ideal if for...

computer algebra Regular element (disambiguation), certain kinds of elements of an algebraic structure Regular extension of fields Regular ideal (multiple definitions)...

ideals that arise from a regular system. Lazard's lemma states that the regular differential and regular algebraic ideals are radical ideals. Regular...

commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its...

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...

no regular hyperbolic star-honeycombs in H3: all forms with a regular star polyhedron as cell, vertex figure or both end up being spherical. Ideal vertices...

chemistry, a regular solution is a solution whose entropy of mixing is equal to that of an ideal solution with the same composition, but is non-ideal due to...

an equidistant surface (a 2-hypercycle), which has two ideal points. Another group of regular polyhedra comprise tilings of the real projective plane...

clerics regular or clerks regular are clerics (mostly priests) who are members of a religious order under a rule of life (regular). Clerics regular differ...

there is no regular sequence in the maximal ideal of length greater than n. More generally, let R be a regular local ring with maximal ideal m. Then any...

(inclusive) then it has an ideal representation, but the triakis tetrahedron is simplicial and non-ideal, and the 4-regular non-ideal example above shows that...

analogues for maximal left ideals and maximal right ideals also hold. For pseudo-rings, the theorem holds for regular ideals. An apparently slightly stronger...

The Canons Regular of St. Augustine are Catholic priests who live in community under a rule (Latin: regula and κανών, kanon, in Greek) and are generally...

In mathematics, specifically ring theory, a principal ideal is an ideal I {\displaystyle I} in a ring R {\displaystyle R} that is generated by a single...

An ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of...

In commutative algebra, the multiplier ideal associated to a sheaf of ideals over a complex variety and a real number c consists (locally) of the functions...

In number theory, an ideal number is an algebraic integer which represents an ideal in the ring of integers of a number field; the idea was developed by...

language is not regular. Syntactic monoid Brzozowski, Janusz; Szykuła, Marek; Ye, Yuli (2018), "Syntactic Complexity of Regular Ideals", Theory of Computing...

one-dimensional ring is necessarily regular. Rendering[clarification needed] a ring normal is known as normalization. If I is an ideal in a commutative ring R, the...

sense. Let T be a regular chain in the polynomial ring R. The saturated ideal sat(T) is an unmixed ideal with dimension n − |T|. A regular chain holds a strong...

{grade}}(I)={\textrm {proj}}\dim(R/I).} A perfect ideal is unmixed. For a regular local ring R {\displaystyle R} a prime ideal I {\displaystyle I} is perfect if and...

an ideal city is the concept of a plan for a city that has been conceived in accordance with a particular rational or moral objective. The "ideal" nature...

{\displaystyle J=\{h\in A|hg\in A\}} , which is an ideal. If x is in D(f), then, since g is regular near x, there is some open affine neighborhood D(h)...

(right) ring ideals. This theory has been studied in great depth. It is known in particular that the direct sum decomposition of the regular representation...

is the Gieseking manifold which is constructed by gluing faces of a regular ideal hyperbolic tetrahedron together. It is also possible to construct a...

Y} of schemes is a regular embedding of codimension r if each point x in X has an open affine neighborhood U in Y such that the ideal of X ∩ U {\displaystyle...

attack on the Fermat problem (see regular prime). Somewhat later again Richard Dedekind formulated the concept of an ideal, Kummer having worked in a different...

Ideal is a British dark comedy television series originally broadcast on TV channel BBC Three, created by Graham Duff and produced by BBC Comedy North...