• In mathematics, an order in the sense of ring theory is a subring O {\displaystyle {\mathcal {O}}} of a ring A {\displaystyle A} , such that A {\displaystyle...
    5 KB (815 words) - 07:53, 7 July 2024
  • In algebra, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those...
    24 KB (3,093 words) - 14:02, 18 May 2025
  • In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the...
    38 KB (6,198 words) - 10:42, 15 May 2025
  • Thumbnail for Ring theory (psychology)
    Ring theory is a concept or paradigm in psychology that recommends a strategy for dealing with the stress a person may feel when someone they encounter...
    10 KB (1,060 words) - 02:12, 2 May 2025
  • order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal...
    13 KB (1,762 words) - 22:38, 17 March 2025
  • Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing...
    31 KB (4,510 words) - 13:16, 14 April 2025
  • or invertible element of a ring is an invertible element for the multiplication of the ring. That is, an element u of a ring R is a unit if there exists...
    11 KB (1,526 words) - 22:40, 5 March 2025
  • group or period of an element Order of a polynomial (disambiguation) Order of a square matrix, its dimension Order (ring theory), an algebraic structure Ordered...
    4 KB (499 words) - 17:14, 31 January 2025
  • Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This...
    32 KB (4,255 words) - 02:03, 6 May 2025
  • on its properties. Commutative algebra, the theory of commutative rings, is a major branch of ring theory. Its development has been greatly influenced...
    99 KB (13,738 words) - 11:06, 29 May 2025
  • In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is...
    19 KB (2,327 words) - 17:43, 12 February 2025
  • of finite rings in their own right has a more recent history. Although rings have more structure than groups do, the theory of finite rings is simpler...
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  • number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group...
    55 KB (8,695 words) - 01:17, 19 May 2025
  • Zero-product property Divisor (ring theory) Integral domain Lam (2001), p. 3 Rowen (1994), p. 99. Some authors also consider the zero ring to be a domain: see Polcino...
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  • elements of the ring or module and is compatible with the ring multiplication. Modules are very closely related to the representation theory of groups. They...
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  • Artinian ring – Ring in abstract algebra Countryman line Order theory – Branch of mathematics Permutation – Mathematical version of an order change Prefix...
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  • The O-ring theory of economic development is a model of economic development put forward by Michael Kremer in 1993, which proposes that tasks of production...
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  • Thumbnail for Algebraic number theory
    supplements introducing the notion of an ideal, fundamental to ring theory. (The word "Ring", introduced later by Hilbert, does not appear in Dedekind's...
    40 KB (5,798 words) - 10:21, 25 April 2025
  • theory the elements of Z {\displaystyle \mathbb {Z} } are often called the "rational integers" because of this. The next simplest example is the ring...
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  • Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing...
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  • model of it is a ring. The standard axiomatization of P A {\displaystyle {\mathsf {PA}}} is more concise and the theory of its order is commonly treated...
    52 KB (8,021 words) - 14:35, 11 April 2025
  • a ring homomorphism. In this case, f is called a ring isomorphism, and the rings R and S are called isomorphic. From the standpoint of ring theory, isomorphic...
    12 KB (1,641 words) - 12:34, 6 May 2025
  • a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity)...
    6 KB (825 words) - 01:18, 19 May 2025
  • assumed (but not excluded, either). Given an integer n, the ring of real square matrices of order n is an example of an associative algebra over the field...
    22 KB (3,122 words) - 20:22, 31 March 2025
  • product. The corresponding idea in module theory is that of a graded module, namely a left module M over a graded ring R such that M = ⨁ i ∈ N M i , {\displaystyle...
    16 KB (2,820 words) - 20:28, 18 May 2025
  • Thumbnail for Pizzagate conspiracy theory
    this theory, a "satanic cabal of elites" of the New World Order operates international child sex trafficking rings. By June 2020, the conspiracy theory found...
    100 KB (8,524 words) - 06:55, 26 May 2025
  • In ring theory, a branch of mathematics, the conductor is a measurement of how far apart a commutative ring and an extension ring are. Most often, the...
    8 KB (1,380 words) - 02:04, 27 April 2023
  • In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model...
    36 KB (5,269 words) - 20:51, 27 December 2024
  • Principal ideal (category Ideals (ring theory))
    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...
    8 KB (1,470 words) - 23:55, 19 March 2025
  • thus called a group Hopf algebra. The apparatus of group rings is especially useful in the theory of group representations. Let G {\displaystyle G} be a...
    21 KB (3,985 words) - 01:23, 3 December 2024