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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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Idempotence is not a medical condition
Communications of the ACM, 2012Messages may be retried. Idempotence means that's OK.
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THE IDEMPOTENTS IN A PERIODIC SEMIGROUP
International Journal of Algebra and Computation, 1996Let [Formula: see text] be the semigroup variety determined by the identity xm=xm+k. For [Formula: see text] we define operations on the set E(S) of idempotents of S and thus obtain the idempotent algebra of S. For any subvariety [Formula: see text] of [Formula: see text] the idempotent algebras of the members of [Formula: see text] form a variety ...
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Fibration of Idempotent Measures
Ukrainian Mathematical Journal, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Idempotent and Hyperassociative Structures
Lobachevskii Journal of Mathematics, 2019An algebra with binary operations is called a binary algebra. A binary algebra \((Q;\Sigma)\) is said to be 1) hyperassociative if \(X(x,Y(y,z))=Y(X(x,y),z)\) for every operations \(X,Y\in\Sigma\), 2) rectangular if \(X(x,X(y,x))=x\) for every operation \(X\in\Sigma\). The main result of the paper under review is Theorem 4.
Movsisyan, Yu., Yolchyan, Marlen
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International Journal of Algebra and Computation, 2004
In this paper we answer a question posed by John Rhodes: "What are the aperiodic-idempotent-pointlike subsemigroups of S?" Answer: Precisely those aperiodic-pointlike subsemigroups that are idempotents, i.e. EPlA(S)={X|X≤E=E2∈PlA(S)}. In the proof we define, for a given variety V (closed under n-tuple expansion) and a given relation R:S-V∈V computing ...
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In this paper we answer a question posed by John Rhodes: "What are the aperiodic-idempotent-pointlike subsemigroups of S?" Answer: Precisely those aperiodic-pointlike subsemigroups that are idempotents, i.e. EPlA(S)={X|X≤E=E2∈PlA(S)}. In the proof we define, for a given variety V (closed under n-tuple expansion) and a given relation R:S-V∈V computing ...
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RADICALS AND IDEMPOTENTS III: q-CENTRAL IDEMPOTENTS
Bulletin of the Australian Mathematical SocietyAbstractPreviously [‘Radicals and idempotents I, II’, Comm. Alg.49(1) (2021), 73–84 and 50(11) (2022), 4791–4804], we have studied the interaction between radicals of rings and idempotents in general or those of particular types, for example, left semicentral.
E. P. COJUHARI, B. J. GARDNER
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