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286
Trigonometric Form of Complex Numbers MML Identifier: COMPTRIG.
"... The scheme Regr without 0 concerns a unary predicate P, and states that: P [1] provided the parameters meet the following requirements: • There exists a non empty natural number k such that P [k], and • For every non empty natural number k such that k � = 1 and P [k] there exists a non empty natural ..."
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z of CF holds z  2 = ℜ(z) 2 + ℑ(z) 2. (8) For all real numbers x1, x2, y1, y2 such that x1 + x2iCF = y1 + y2iCF holds x1 = y1 and x2 = y2. (9) For every element z of CF holds z = ℜ(z) + ℑ(z)iCF. (10) 0CF = 0 + 0iCF. (12) 2 For every unital non empty groupoid L and for every element x of L holds
A NONHAUSDORFF ÉTALE GROUPOID
, 812
"... We present an example of a nonHausdorff, étale, essentially principal groupoid for which two results, known to hold in the Hausdorff case, fail. These results are: (A) the subalgebra of continuous functions on the unit space is maximal abelian, and (B) every nontrivial ideal of the reduced groupoid ..."
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Cited by 7 (2 self)
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We present an example of a nonHausdorff, étale, essentially principal groupoid for which two results, known to hold in the Hausdorff case, fail. These results are: (A) the subalgebra of continuous functions on the unit space is maximal abelian, and (B) every nontrivial ideal of the reduced
ON PRIME LEFT(RIGHT) IDEALS OF GROUPOIDSORDERED GROUPOIDS
, 2004
"... Abstract. Recently, Kehayopulu and Tsingelis studied for prime ideals of groupoidsordered groupoids. In this paper, we give some results on prime left(right) ideals of groupoidordered groupoid. These results are generalizations of their results. If (G, ·,≤) is an ordered groupoid, a nonempty subs ..."
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Abstract. Recently, Kehayopulu and Tsingelis studied for prime ideals of groupoidsordered groupoids. In this paper, we give some results on prime left(right) ideals of groupoidordered groupoid. These results are generalizations of their results. If (G, ·,≤) is an ordered groupoid, a nonempty
RELATIVE FROBENIUS ALGEBRAS ARE GROUPOIDS
"... Abstract. We functorially characterize groupoids as special dagger Frobenius algebras in the category of sets and relations. This is then generalized to a nonunital setting, by establishing an adjunction between H*algebras in the category of sets and relations, and locally cancellative regular sem ..."
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Cited by 5 (3 self)
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Abstract. We functorially characterize groupoids as special dagger Frobenius algebras in the category of sets and relations. This is then generalized to a nonunital setting, by establishing an adjunction between H*algebras in the category of sets and relations, and locally cancellative regular
Relative Frobenius algebras are groupoids
"... We functorially characterize groupoids as special dagger Frobenius algebras in the category of sets and relations. This is then generalized to a nonunital setting, by establishing an adjunction between H*algebras in the category of sets and relations, and locally cancellative regular semigroupoids ..."
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We functorially characterize groupoids as special dagger Frobenius algebras in the category of sets and relations. This is then generalized to a nonunital setting, by establishing an adjunction between H*algebras in the category of sets and relations, and locally cancellative regular
Classifying groupoids and semirings of finite order
, 2005
"... Given a nonempty finite set S = {e1, e2,..., em} and a binary operation B on S, i.e. B: S × S → S. For arbitrary elements a, b, c ∈ S we write aBb = c instead of B: (a, b) 7 → c. The pair (S,B) is called a groupoid, ..."
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Given a nonempty finite set S = {e1, e2,..., em} and a binary operation B on S, i.e. B: S × S → S. For arbitrary elements a, b, c ∈ S we write aBb = c instead of B: (a, b) 7 → c. The pair (S,B) is called a groupoid,
Finite quantum groupoids and inclusion of finite type
 Fields Institute Communications
, 2000
"... In the last decade various motivations coming from low dimensional quantum field theory, operator algebra, and Poisson geometry have lead to the introduction of a new notion of symmetry that generalizes both quantum groups and classical groupoid algebras. The slightly different definitions [18, 29, ..."
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Cited by 36 (7 self)
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representation in the monoidal category MA of Amodules. In the groupoid interpretation A L and A R are noncommutative analogues of the algebra of functions on the space of units. The various definitions of quantum groupoid differ in the size and in commutativity of these subalgebras. The most general among
A.S.Muktibodh, Some results on Smarandache groupoids
 Scientia Magna ,Vol.8
"... Abstract In this paper we prove some results towards classifying Smarandache groupoids which are in Z∗(n) and not in Z(n) when n is even and n is odd. Keywords Groupoids, Smarandache groupoids. §1. Introduction and preliminaries In [3] and [4], W. B. Kandasamy defined new classes of Smarandache grou ..."
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Cited by 1 (0 self)
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groupoids using Zn. In this paper we prove some theorems for construction of Smarandache groupoids according as n is even or odd. Definition 1.1. A nonempty set of elements G is said to form a groupoid if in G is
A nonamenable groupoid whose maximal and reduced C * algebras are the same
"... Abstract We construct a locally compact groupoid with the properties in the title. Our example is based closely on constructions used by Higson, Lafforgue, and Skandalis in their work on counterexamples to the BaumConnes conjecture. It is a bundle of countable groups over the one point compactifica ..."
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Abstract We construct a locally compact groupoid with the properties in the title. Our example is based closely on constructions used by Higson, Lafforgue, and Skandalis in their work on counterexamples to the BaumConnes conjecture. It is a bundle of countable groups over the one point
A HYPEROPERATION DEFINED ON A GROUPOID EQUIPPED WITH A MAP
"... The Hvstructures are hyperstructures where the equality is replaced by the nonempty intersection. The fact that this class of the hyperstructures is very large, one can use it in order to define several objects that they are not possible to be defined in the classical hypergroup theory. In the pre ..."
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Cited by 1 (1 self)
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The Hvstructures are hyperstructures where the equality is replaced by the nonempty intersection. The fact that this class of the hyperstructures is very large, one can use it in order to define several objects that they are not possible to be defined in the classical hypergroup theory
Results 1  10
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286