Ideal theory information

In mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much...

Ideal observer theory is the meta-ethical view which claims that ethical sentences express truth-apt propositions about the attitudes of a hypothetical...

typical of Rawls' approach that he focuses on ideal theory and does not discuss to any great extent non-ideal theory, which involves considering the proper response...

theory, the ideal class group (or class group) of an algebraic number field K is the quotient group JK /PK where JK is the group of fractional ideals...

Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both...

domains. Hence the theory of fractional ideals can be described for the rings of integers of number fields. In fact, class field theory is the study of such...

and specifically metaphysics, the theory of Forms, theory of Ideas, Platonic idealism, or Platonic realism is a theory widely credited to the Classical...

Rawlsianism” and its “ideal theory” against the actual history of racialized oppression in the modern era, and proposes that non-ideal theory is urgently needed...

theory Ideal theory Index theory Information theory Invariant theory Iwasawa theory K-theory Knot theory L-theory Lattice theory Lie theory M-theory Measure...

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

substance; and R {\displaystyle R} is the ideal gas constant. It can also be derived from the microscopic kinetic theory, as was achieved (apparently independently)...

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...

factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory, like the existence of solutions...

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...

studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent...

mathematics, specifically ring theory, a left primitive ideal is the annihilator of a (nonzero) simple left module. A right primitive ideal is defined similarly...

theory — Galois theory — Game theory — Gauge theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal theory —...

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...

the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures...

abstract algebra and early ideal theory and valuation theory; see below. A conventional starting point for analytic number theory is Dirichlet's theorem on...

In ring theory, a branch of mathematics, the radical of an ideal I {\displaystyle I} of a commutative ring is another ideal defined by the property that...

In number theory, the fundamental theorem of ideal theory in number fields states that every nonzero proper ideal in the ring of integers of a number...

commutative algebra Krull's principal ideal theorem Regular local ring Matsumura, Hideyuki: "Commutative Ring Theory", page 30–31, 1989 Eisenbud, D. Commutative...

both the Newtonian dynamics (as in "kinetic theory") and in quantum mechanics (as a "gas in a box"). The ideal gas model has also been used to model the...

actively pursues as goals Platonic ideal, a philosophical idea of trueness of form, associated with Plato Ideal (ring theory), special subsets of a ring considered...

paper Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains), Noether developed the theory of ideals in commutative rings into a tool with...