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Rectangular groupoids and related structures.
Discrete Math, 2013 Boykett T.
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On the importance of idempotence
Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing, 2006Range searching is among the most fundamental problems in computational geometry. An n-element point set in Rd is given along with an assignment of weights to these points from some commutative semigroup. Subject to a fixed space of possible range shapes, the problem is to preprocess the points so that the total semigroup sum of the points lying within
Sunil Arya +2 more
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On idempotency of linear combinations of idempotent matrices
Applied Mathematics and Computation, 2004Let \(P_1, P_2\) and \(P_3\) being any three different nonzero mutually commutative \(n\times n\) idempotent matrices, and \(c_1,c_2\) and \(c_3\) being nonzero scalars, the problem of characterizing some situations, where a linear combination of the form \(P=c_1P_1+c_2P_2\) or \(P=c_1P_1+c_2P_2+c_3P_3\), is also an idempotent matrix is considered ...
Halim Özdemir, Ahmet Yasar Özban
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The Review of Symbolic Logic, 2013
AbstractA 1-ary sentential context is aggregative (according to a consequence relation) if the result of putting the conjunction of two formulas into the context is a consequence (by that relation) of the results of putting first the one formula and then the other into that context.
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AbstractA 1-ary sentential context is aggregative (according to a consequence relation) if the result of putting the conjunction of two formulas into the context is a consequence (by that relation) of the results of putting first the one formula and then the other into that context.
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ON THE IDEMPOTENCY AND CO-IDEMPOTENCY OF THE MORPHOLOGICAL CENTER
International Journal of Pattern Recognition and Artificial Intelligence, 2001By a novel use of distributivity we obtain polynomial time algorithms to decide whether or not a given min–max operator (stack filter) is idempotent or not. Several properties related to idempotency can also be tested in polynomial time. In particular we apply these results to the morphological center of two operators.
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DISTRIBUTIVE IDEMPOTENT UNINORMS
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2003A characterization of all idempotent uninorms satisfying the distributive property is given. The special cases of left-continuous and right-continuous idempotent uninorms are presented separately and it is also proved that all idempotent uninorms are autodistributive.
Daniel Ruiz 0001, Joan Torrens
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Mathematical Logic Quarterly, 1986
DeMorgan monoids stand to the relevant logic R as Boolean algebras do to classical logic, or as Heyting lattices do to intuitionistic logic. By an idempotent in a DeMorgan monoid we mean an element a such that \(a\circ a=a\), where \(\circ\) is the fusion (or consistency) operation defined by \(b\circ c=\sim (b\to \sim c)\).
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DeMorgan monoids stand to the relevant logic R as Boolean algebras do to classical logic, or as Heyting lattices do to intuitionistic logic. By an idempotent in a DeMorgan monoid we mean an element a such that \(a\circ a=a\), where \(\circ\) is the fusion (or consistency) operation defined by \(b\circ c=\sim (b\to \sim c)\).
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European Journal of Operational Research, 1999
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QUASIVARIETIES OF IDEMPOTENT SEMIGROUPS
International Journal of Algebra and Computation, 2003It is proved that the lattice L(Bd) of quasivarieties contained in the variety Bdof idempotent semigroups contains an isomorphic copy of the ideal lattice of a free lattice on ω free generators. This result shows that a problem of Petrich [19], which calls for a description of L(Bd), is much more complex than originally expected.
M. E. Adams, Wieslaw Dziobiak
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Canadian Mathematical Bulletin, 1974
Let N be an ideal of a ring A. We say that idempotents modulo N can be lifted provided that for every a of A such that a2-a ∈ N there exists an element e2=e ∈ A such that e-a ∈ N. The technique of lifting idempotents is considered to be a fundamental tool in the classical theory of nonsemiprimitive Artinian rings (refer [2; p. 72]).
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Let N be an ideal of a ring A. We say that idempotents modulo N can be lifted provided that for every a of A such that a2-a ∈ N there exists an element e2=e ∈ A such that e-a ∈ N. The technique of lifting idempotents is considered to be a fundamental tool in the classical theory of nonsemiprimitive Artinian rings (refer [2; p. 72]).
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