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The maximal subsemigroups of the ideals of some semigroups of partial injections

Ilinka Dimitrova, Jörg Koppitz (2009)

Discussiones Mathematicae - General Algebra and Applications

We study the structure of the ideals of the semigroup I O n of all isotone (order-preserving) partial injections as well as of the semigroup I M n of all monotone (order-preserving or order-reversing) partial injections on an n-element set. The main result is the characterization of the maximal subsemigroups of the ideals of I O n and I M n .

The Milgram non-operad

Michael Brinkmeier (1999)

Annales de l'institut Fourier

C. Berger claimed to have constructed an E n -operad-structure on the permutohedras, whose associated monad is exactly the Milgram model for the free loop spaces. In this paper I will show that this statement is not correct.

The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz

J. Dudek (1996)

Colloquium Mathematicae

The main result of this paper is a description of totally commutative idempotent groupoids. In particular, we show that if an idempotent groupoid (G,·) has precisely m ≥ 2 distinct essentially binary polynomials and they are all commutative, then G contains a subgroupoid isomorphic to the groupoid N m described below. In [2], this fact was proved for m = 2.

The minimizing of the Nielsen root classes

Daciberg Gonçalves, Claudemir Aniz (2004)

Open Mathematics

Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen...

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