abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups...
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Commonly studied types of magma include: Quasigroup: A magma where division is always possible. Loop: A quasigroup with an identity element. Semigroup: A...
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a CH-quasigroup, introduced by Manin (1986, definition 1.3), is a symmetric quasigroup in which any three elements generate an abelian quasigroup. "CH"...
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with quasigroups, which are generalization of groups in a different direction; the operation in a quasigroup need not be associative but quasigroups preserve...
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2004, as a part of his PhD dissertation entitled Totally Antisymmetric Quasigroups. The Damm algorithm is similar to the Verhoeff algorithm. It too will...
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Associator (section Quasigroup theory)
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...
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In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems. As in other areas of...
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Latin squares and quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraic....
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then the rows are orthogonal. In fact, small category is orthogonal to quasigroup, and groupoid is orthogonal to magma. Consequently there are zeros in...
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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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Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
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of X. Free loop Loop group Loop space Loop algebra Fundamental group Quasigroup Adams, John Frank (1978), Infinite Loop Spaces, Annals of mathematics...
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Identity (equation) Identity function Inverse element Monoid Pseudo-ring Quasigroup Unital (disambiguation) Weisstein, Eric W. "Identity Element". mathworld...
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commutative. Quasigroup: a magma obeying the Latin square property. A quasigroup may also be represented using three binary operations. Loop: a quasigroup with...
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Unneeded Unneeded Unneeded Required Quasigroup Required Unneeded Unneeded Required Unneeded Commutative quasigroup Required Unneeded Unneeded Required...
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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...
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Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
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Unneeded Unneeded Unneeded Required Quasigroup Required Unneeded Unneeded Required Unneeded Commutative quasigroup Required Unneeded Unneeded Required...
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Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
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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...
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Moufang loop (section Moufang quasigroups)
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...
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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...
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Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
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Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
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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...
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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;...
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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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quasigroup, IP-quasigroup, F-quasigroups, CI-quasigroup, I-quasigroups Bol loops, totally symmetric quasigroups and quasigroup Stein et al.) Quasigroups a balanced...
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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)...
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conjecture ADHM construction Gauss–Manin connection Cartier–Manin operator CH-quasigroup Modular symbol Quantum simulator Awards Nemmers Prize in Mathematics (1994)...
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