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Existence of invariant idempotent measures by contractivity of idempotent Markov operators
We prove that the idempotent Markov operator generated by contractive max plus normalized iterated function system (IFS) is also a contractive map...
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Multiplicatively Idempotent Semirings with Annihilator Condition
Abstract—The structural theory of semirings with additional conditions is considered. Multiplicatively idempotent semirings with the annihilator...
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Invariant measures for place-dependent idempotent iterated function systems
We study the set of invariant idempotent probabilities for place-dependent idempotent iterated function systems defined in compact metric spaces....
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Abstract factorization theorems with applications to idempotent factorizations
Let ⪯ be a preorder on a monoid H with identity 1 H and s be an integer ≥ 2. The ⪯-height of an element x ∈ H is the supremum of the integers k ≥ 1...
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Functor of Idempotent Probability Measures with Compact Support and Open Map**s
In this paper, we show that the functor of idempotent probability measures with compact support acting in the category of Tikhonov spaces and their...
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Large sets near idempotent and its product
Tootkaboni and Vahed introduced the notion of some large sets near idempotent along with some combinatorial properties. We characterize when the...
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Multiplicatively Idempotent Semirings in which All Congruences Are Ideal
AbstractThe study of multiplicatively idempotent semirings with additional conditions is continued. It is proved that every multiplicatively...
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Completely Prime Ideals in Multiplicatively Idempotent Semirings
AbstractStructure properties of multiplicatively idempotent semirings are considered. Basic results concerning completely prime ideals in...
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Mixed Idempotent Abelian Groups
An Abelian group is called idempotent if any element is idempotent for some multiplication. This paper contains a complete description of...
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Idempotent Varieties of Incidence Monoids and Bipartite Posets
The algebraic variety defined by the idempotents of an incidence monoid is investigated. Its irreducible components are determined. The intersection...
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Pre-Lie Algebras, Their Multiplicative Lattice, and Idempotent Endomorphisms
We introduce the notions of pre-morphism and pre-derivation for arbitrary non-associative algebras over a commutative ring k with identity. These...
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Dynamics of Quadratic Operators of Idempotent Measures
AbstractWe study dynamical systems generated by some quadratic operators, map** the simplex of idempotent measures to itself. The types of fixed...
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Definable convolution and idempotent Keisler measures
We initiate a systematic study of the convolution operation on Keisler measures, generalizing the work of Newelski in the case of types. Adapting...