• Thumbnail for Quasigroup
    abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups...
    31 KB (3,860 words) - 01:49, 23 September 2024
  • Commonly studied types of magma include: Quasigroup: A magma where division is always possible. Loop: A quasigroup with an identity element. Semigroup: A...
    18 KB (1,836 words) - 08:15, 24 September 2024
  • a CH-quasigroup, introduced by Manin (1986, definition 1.3), is a symmetric quasigroup in which any three elements generate an abelian quasigroup. "CH"...
    651 bytes (59 words) - 12:51, 4 October 2024
  • Thumbnail for Semigroup
    with quasigroups, which are generalization of groups in a different direction; the operation in a quasigroup need not be associative but quasigroups preserve...
    37 KB (4,677 words) - 01:13, 9 September 2024
  • 2004, as a part of his PhD dissertation entitled Totally Antisymmetric Quasigroups. The Damm algorithm is similar to the Verhoeff algorithm. It too will...
    12 KB (1,089 words) - 06:55, 4 February 2024
  • n,R]=[R,R,n]=\{0\}\ .} The nucleus is an associative subring of R. A quasigroup Q is a set with a binary operation ⋅ : Q × Q → Q {\displaystyle \cdot...
    3 KB (488 words) - 02:09, 13 May 2024
  • In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems. As in other areas of...
    30 KB (3,559 words) - 18:14, 9 February 2024
  • Latin squares and quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraic....
    26 KB (3,503 words) - 08:47, 10 August 2024
  • then the rows are orthogonal. In fact, small category is orthogonal to quasigroup, and groupoid is orthogonal to magma. Consequently there are zeros in...
    14 KB (1,939 words) - 03:02, 14 September 2024
  • a⁻¹ ∗ (a ∗ c) which implies b = c by associativity. For example, every quasigroup, and thus every group, is cancellative. To say that an element a in a...
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  • Thumbnail for Monoid
    Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
    35 KB (4,447 words) - 08:24, 16 July 2024
  • Thumbnail for Loop (topology)
    of X. Free loop Loop group Loop space Loop algebra Fundamental group Quasigroup Adams, John Frank (1978), Infinite Loop Spaces, Annals of mathematics...
    1 KB (130 words) - 07:12, 17 May 2022
  • Identity (equation) Identity function Inverse element Monoid Pseudo-ring Quasigroup Unital (disambiguation) Weisstein, Eric W. "Identity Element". mathworld...
    10 KB (737 words) - 22:11, 6 July 2024
  • commutative. Quasigroup: a magma obeying the Latin square property. A quasigroup may also be represented using three binary operations. Loop: a quasigroup with...
    19 KB (2,223 words) - 21:00, 23 September 2024
  • Thumbnail for Category (mathematics)
    Unneeded Unneeded Unneeded Required Quasigroup Required Unneeded Unneeded Required Unneeded Commutative quasigroup Required Unneeded Unneeded Required...
    21 KB (2,521 words) - 21:37, 12 August 2024
  • Thumbnail for Division (mathematics)
    unique for all a and all b (the Latin square property) is a quasigroup. In a quasigroup, division in this sense is always possible, even without an identity...
    25 KB (3,476 words) - 14:18, 22 September 2024
  • Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
    16 KB (2,819 words) - 14:00, 30 September 2024
  • Unneeded Unneeded Unneeded Required Quasigroup Required Unneeded Unneeded Required Unneeded Commutative quasigroup Required Unneeded Unneeded Required...
    39 KB (6,202 words) - 03:00, 10 July 2024
  • Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
    20 KB (2,773 words) - 10:09, 18 February 2024
  • ambient space, which carries one subset to the other Isotopy of quasigroups. See Quasigroup#Homotopy and isotopy. Isotopy of loops, a triple of maps with...
    989 bytes (163 words) - 10:28, 23 December 2021
  • generalized to Moufang loops by Stephen Gagola III in recent years. Any quasigroup satisfying one of the Moufang identities must, in fact, have an identity...
    11 KB (1,738 words) - 21:03, 14 April 2024
  • medial quasigroup under this operation. The Bruck–Toyoda theorem states that every medial quasigroup is of this form, i.e. is isomorphic to a quasigroup defined...
    7 KB (864 words) - 13:08, 26 March 2024
  • Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
    20 KB (2,691 words) - 00:21, 24 September 2024
  • Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
    19 KB (2,440 words) - 15:00, 29 May 2024
  • However, Cayley tables can also be used to characterize the operation of a quasigroup, which does not assume associativity as an axiom (indeed, Cayley tables...
    10 KB (1,048 words) - 05:20, 4 October 2024
  • Thumbnail for Group (mathematics)
    Wiesław A. (2001), "On some old and new problems in n-ary groups" (PDF), Quasigroups and Related Systems, 8: 15–36, MR 1876783. Eliel, Ernest; Wilen, Samuel;...
    101 KB (13,147 words) - 02:07, 28 September 2024
  • one can count to on one's fingers using senary. 35 is the number of quasigroups of order 4. 35 is the smallest composite number of the form 6 k + 5 {\displaystyle...
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  • Thumbnail for Valentin Belousov
    quasigroup, IP-quasigroup, F-quasigroups, CI-quasigroup, I-quasigroups Bol loops, totally symmetric quasigroups and quasigroup Stein et al.) Quasigroups a balanced...
    11 KB (1,340 words) - 13:32, 27 March 2024
  • isotope of an algebra: see Isotopy of algebras An isotope of a loop or quasigroup: see Isotopy of loops Isotone Isotropy, an unrelated concept Isotype (disambiguation)...
    1 KB (192 words) - 21:41, 17 November 2022
  • Thumbnail for Yuri Manin
    conjecture ADHM construction Gauss–Manin connection Cartier–Manin operator CH-quasigroup Modular symbol Quantum simulator Awards Nemmers Prize in Mathematics (1994)...
    20 KB (1,550 words) - 21:30, 4 October 2024