- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 15:16:57
5
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PM&vol=69&iss=4&update_since=2024-03-29
Portugaliae Mathematica
Port. Math.
PM
0032-5155
1662-2758
General
10.4171/PM
http://www.ems-ph.org/doi/10.4171/PM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2008)
69
2012
4
Construction of $n$-ary $(H,G)$-hypergroups
Said
Anvariyeh
Yazd University, YAZD, IRAN
Bijan
Davvaz
Yazd University, YAZD, IRAN
Saeed
Mirvakili
Payame Noor University, TEHRAN, IRAN
$n$-ary hypergroup, $n$-ary $(H,G)$-hypergroups, complete part
In this paper, we shall define the concepts of completion and complete part with respect to $n$-ary $(H,G)$-hypergroups. Moreover, we present a way to obtain a new $n$-ary hypergroup, starting with other $n$-ary hypergroups. Finally, we introduce the fundamental relation of an $n$-ary hypergroup and prove some results. Examples in known classes of $n$-ary $(H,G)$-hypergroups are also investigated.
Group theory and generalizations
General
259
281
10.4171/PM/1917
http://www.ems-ph.org/doi/10.4171/PM/1917
On perfect polynomials over $\mathbb{F}_p$ with $p$ irreducible factors
Luis
Gallardo
Université de Brest, BREST CEDEX 3, FRANCE
Olivier
Rahavandrainy
Université de Brest, BREST CEDEX 3, FRANCE
Sum of divisors, polynomials, finite fields, characteristic $p$
We consider, for a fixed odd prime number $p$, monic polynomials in one variable over the finite field $\mathbb{F}_p$ which are equal to the sum of their monic divisors. Call them \emph{perfect} polynomials. We prove that the exponents of each irreducible factor of any perfect polynomial having no root in $\mathbb{F}_p$ and $p$ irreducible factors are all less than $p-1$. We completely characterize those perfect polynomials for which each irreducible factor has degree two and all exponents do not exceed two.
Number theory
General
283
303
10.4171/PM/1918
http://www.ems-ph.org/doi/10.4171/PM/1918
Class $wA(s,t)$ operators and quasisimilarity
Mohammad H. M.
Rashid
Faculty of Science, Mu’tah University, AL-KARAK, JORDAN
Class $wA(s,t)$ operators, Fuglede–Putnam Theorem, quasisimilarity
In this paper it is shown that the normal parts of quasisimilar $wA(s,t)$ operators with $s+t=1$ are unitarily equivalent. Also, we establish the orthogonality of the range and the kernel of a nonnormal derivation with respect to the unitarily invariant norms associated with norm ideals of operators. Moreover, we obtain that the range of the generalized derivation induced by an pair satisfies Fuglede–Putnam property is orthogonal to its kernel.
Operator theory
General
305
320
10.4171/PM/1919
http://www.ems-ph.org/doi/10.4171/PM/1919
Regularities and limit theorems of some additive functionals of symmetric stable process in some anisotropic Besov spaces
Aissa
Sghir
Faculté des Sciences, Université Mohammed I, OUJDA, MOROCCO
Hanae
Ouahhabi
Faculté des Sciences, Université Mohammed I, OUJDA, MOROCCO
Anisotropic Besov space, symmetric stable process, fractional Brownian motion, fractional derivative, additive functional, slowly varying function
In this paper, we give some regularities and limit theorems of some additive functionals of symmetric stable process of index $1
Probability theory and stochastic processes
General
321
339
10.4171/PM/1920
http://www.ems-ph.org/doi/10.4171/PM/1920
Krohn–Rhodes complexity of Brauer type semigroups
Karl
Auinger
Universität Wien, WIEN, AUSTRIA
Krohn–Rhodes complexity, Brauer type semigroup, pseudovariety of finite semigroups
The Krohn–Rhodes complexity of the Brauer type semigroups $\mathfrak{B}_n$ and $\mathfrak{A}_n$ is computed. In three-quarters of the cases the result is the ‘expected’ one: the complexity coincides with the (essential) $\mathcal{J}$-depth of the respective semigroup. The exception (and perhaps the most interesting case) is the annular semigroup $\mathfrak{A}_{2n}$ of even degree in which case the complexity is the $\mathcal{J}$-depth minus $1$. For the ‘rook’ versions $P\mathfrak{B}_n$ and $P\mathfrak{A}_n$ it is shown that $c(P\mathfrak{B}_n)=c(\mathfrak{B}_n)$ and $c(P\mathfrak{A}_{2n-1})=c(\mathfrak{A}_{2n-1})$ for all $n\ge 1$. The computation of $c(P\mathfrak{A}_{2n})$ is left as an open problem.
Group theory and generalizations
General
341
360
10.4171/PM/1921
http://www.ems-ph.org/doi/10.4171/PM/1921