Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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TL;DR: This paper presents an embedding of NL into an idempotent semiring of intervals, which allows to extend NL from single intervals to sets of intervals as well as to extend the approach to arbitrary idemPotent semirings.
4 citations
TL;DR: For positive matrices with a positive commutator, this article showed that the dimension of the unital algebra generated by the matrices is at most n (n + 1 ) 2 and that this bound can be attained.
4 citations
TL;DR: A finitely based equational class of idempotent algebras of type,m, n ≥ 2, is two-based as mentioned in this paper, and any class of ǫ-based equational classes with m ≥ 2 and k ≥ 2 is k-based.
Abstract: A finitely based equational class of idempotent algebras of type ,m, n≥2, is two-based. More generally, any finitely based equational class of idempotent algebras of type withm
i≥2 andk≥2 isk-based.
4 citations
TL;DR: The aim of the present paper is to determine the lattice of all varieties of idempotent and distributive semirings with involution, and it turns out that it has exactly 64 elements.
Abstract: A semiring with involution is a semiring equipped with an involutorial antiasutomorphism as a fundamental operation. The aim of the present paper is to determine the lattice of all varieties of idempotent and distributive semirings with involution. We start with the description of their structure, which is followed by a complete list of all subdirectly irreducibles. We make a heavy use of general results obtained recently by Dolinka and Vincic [11] on involutorial Plonka sums. Applying these results and some further structural theorems, we construct the considered lattice. It turns out that it has exactly 64 elements.
4 citations
TL;DR: In this paper, the abstract concavity and support set of extended valued elementary topical functions are characterized for the upward and downward sets of a b-complete idempotent semimodule.
Abstract: In this article, we study topical functions f:X→K defined on a b-complete idempotent semimodule X over a b-complete idempotent semifield K with values in K. We characterize the abstract concavity and support set of this class of functions. Next, we investigate the abstract concavity of extended valued topical functions , where and ⊤: = supK. Finally, as an application, we present characterizations of upward and downward sets by using extended valued elementary topical functions.
4 citations