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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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Journal ArticleDOI
TL;DR: In this paper, the hyperpower method is generalized by insizing an idempotent matrix P. The convergence behavior of Bqk is analyzed and the results are applied to give a detailed investigation of this iteration.

13 citations

Journal ArticleDOI
TL;DR: In this note, some equivalents are established of the Drazin invertibility of differences and sums of idempotent operators on a Hilbert space.

13 citations

Book ChapterDOI
27 Aug 2012
TL;DR: Almeida and Azevedo as discussed by the authors showed that the join of deterministic and codeterministic products is decidable; this is the first non-trivial join level of the Trotter-Weil hierarchy.
Abstract: The variety DA of finite monoids has a huge number of different characterizations, ranging from two-variable first-order logic FO2 to unambiguous polynomials. In order to study the structure of the subvarieties of DA, Trotter and Weil considered the intersection of varieties of finite monoids with bands, i.e., with idempotent monoids. The varieties of idempotent monoids are very well understood and fully classified. Trotter and Weil showed that for every band variety V there exists a unique maximal variety W inside DA such that the intersection with bands yields the given band variety V. These maximal varieties W define the Trotter-Weil hierarchy. This hierarchy is infinite and it exhausts DA; induced by band varieties, it naturally has a zigzag shape. In their paper, Trotter and Weil have shown that the corners and the intersection levels of this hierarchy are decidable. In this paper, we give a single identity of omega-terms for every join level of the Trotter-Weil hierarchy; this yields decidability. Moreover, we show that the join levels and the subsequent intersection levels do not coincide. Almeida and Azevedo have shown that the join of $\mathcal R$-trivial and $\mathcal L$-trivial finite monoids is decidable; this is the first non-trivial join level of the Trotter-Weil hierarchy. We extend this result to the other join levels of the Trotter-Weil hierarchy. At the end of the paper, we give two applications. First, we show that the hierarchy of deterministic and codeterministic products is decidable. And second, we show that the direction alternation depth of unambiguous interval logic is decidable.

13 citations

Posted Content
TL;DR: This article proves that the set of all idempotents with certain fixed points is a semiring and finds its order, and shows that this semiring is an ideal in a well-known semiring.
Abstract: Idempotents yield much insight in the structure of finite semigroups and semirings. In this article, we obtain some results on (multiplicatively) idempotents of the endomorphism semiring of a finite chain. We prove that the set of all idempotents with certain fixed points is a semiring and find its order. We further show that this semiring is an ideal in a well known semiring. The construction of an equivalence relation such that any equivalence class contain just one idempotent is proposed. In our main result we prove that such equivalence class is a semiring and find his order. We prove that the set of all idempotents with certain jump points is a semiring.

13 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023106
2022263
202184
2020100
201991
201892