2,886 research outputs found
Network Code on Requirements for Generators – a Discussion. Resynchronizing with paradigm shifts
No full textThe Network Code on Requirements for Generators, known also as RfG, is the most recent document approved by the European Commission that recommends the technical conditions for connection and operation of all types of generators in the ENTSO-E zone. Although RfG was published in the Official EU Journal in 2016, each EU member country is responsible to adopt it in the form that best suits to its characteristics. Therefore, the latest achievements in deployment of storage and renewables technologies should be also considered. Moreover, the new concepts included in the EU winter package (2016) for empowering the citizen and encouraging prosumer’s self-consumption, resilience and efficiency requires careful analysis of the document. This paper aims at identifying some shortcomings of the proposed document, based on latest technology advancements and societal aspirations, and proposes a new approach that allows synchronizing the new network codes with the smart grids paradigm shift
Field Theoretic Cogalois Theory via Abstract Cogalois Theory
No full textAbstractAbstract Cogalois Theory for arbitrary profinite groups was initiated by T. Albu and Ş.A. Basarab [An Abstract Cogalois Theory for profinite groups, J. Pure. Appl. Algebra 200 (2005) 227–250]. The aim of this paper is twofold: firstly, to present the abstract group theoretic versions of various types of Kummer field extensions, and secondly, to show how some basic results of the (Field Theoretic) Cogalois Theory can be very easily deduced from their abstract versions
Finite Radical Field Extensions and Crossed Homomorphisms
No full textAbstractWe extend to arbitrary finite radical extensions the results of Barrera-Mora and Velez (J. Algebra162(1993), 295–301) concerning simple radical extensions and we obtain in terms of crossed homomorphisms new characterizations of Kneser extensions andΔ-Cogalois extensions introduced by Albu and Nicolae (J. Number Theory52(1995), 299–318)
Lattice-Isomorphic Groups, and Infinite Abelian <i>g</I>-cogalois Field Extensions
No full textThe aim of this paper is to provide a proof of the following result claimed by Albu (Infinite field extensions with Galois-Cogalois correspondence (II), Revue Roumaine Math. Pures Appl. 47 (2002), to appear): The Kneser group Kne(E/F) of an Abelian G-Cogalois extension E/F and the group of continuous characters Ch(Gal(E/F)) of its Galois group Gal(E/F) are isomorphic (in a noncanonical way). The proof we give in this paper explains why such an isomorphism is expected, being based on a classical result of Baer (Amer. J. Math. 61 (1939), 1-44) devoted to the existence of group isomorphisms arising from lattice isomorphisms of their lattices of subgroups.Alexander von Humboldt Foundation; Consiliul National al Cercetarii Stiintifice din Invatamantul Superior, Romania; grant of Romanian AcademyThis work was completed during the stay of the first author at the Heinrich-Heine University of Dusseldorf as a Humboldt Fellow in April-June 2001. He is very indebted to the University for hospitality and to the Alexander von Humboldt Foundation for financial support. He gratefully acknowledges partial support from grant D-7 awarded by the Consiliul National al Cercetarii Stiintifice din Invatamantul Superior, Romania. He would also like to thank Mihai Sabac for helpful discussions on characters of locally compact Abelian groups.r The second author gratefully acknowledges partial support from a grant of the Romanian Academy
An indecomposable nonlocally finitely generated Grothendieck category with simple objects
No full textAbstractA Grothendieck category C is said to be locally finitely generated if the subobject lattice of every object in C is compactly generated, or equivalently, if C possesses a family of finitely generated generators. Every nonzero locally finitely generated Grothendieck category possesses simple objects. We shall call a Grothendieck category C indecomposable if C is not equivalent to a product of nonzero Grothendieck categories C1×C2. In this paper an example of an indecomposable nonlocally finitely generated Grothendieck category possessing simple objects is constructed, answering in the negative a sharper form of a question posed by Albu, Iosif, and Teply in [T. Albu, M. Iosif, M.L. Teply, Dual Krull dimension and quotient finite dimensionality, J. Algebra 284 (2005) 52–79]
Dual Krull dimension and quotient finite dimensionality
No full textAbstractA modular lattice L with 0 and 1 is called quotient finite dimensional (QFD) if [x,1] has no infinite independent set for any x∈L. We characterize upper continuous modular lattices L that have dual Krull dimension k0(L)⩽α, by relating that with the property of L being QFD and with other conditions involving subdirectly irreducible lattices and/or meet irreducible elements. In particular, we answer in the positive, in the more general latticial setting, some open questions on QFD modules raised by Albu and Rizvi [Comm. Algebra 29 (2001) 1909–1928]. Applications of these results are given to Grothendieck categories and module categories equipped with a torsion theory
Strongly fully invariant-extending modular lattices
No full textThis paper is a natural continuation of our previous joint paper [Albu, Kara, Tercan, Fully invariant-extending modular lattices, and applications (I), J. Algebra 517 (2019), 207-222], where we introduced and investigated the notion of a fully invariant-extending lattice, the latticial counterpart of a fully invariant-extending module. In this paper we introduce and investigate the latticial counter-part of the concept of a strongly FI-extending module defined by Birkenmeier, Park, Rizvi (2002) as a module M having the property that every fully invariant submodule of M is essential in a fully invariant direct summand of M. Our main tool in doing so, is again the very useful concept of a linear morphism of lattices introduced in the literature by Albu and Iosif (2013)
Infinite Cogalois Theory, Clifford Extensions, and Hopf Algebras
No full textThe aim of this paper is to present some connections of infinite Cogalois Theory with Clifford extensions and Hopf algebras.Alexander von Humboldt-StiftungThis work was started during the stay of the author at the Heinrich-Heine-University of Dusseldorf as a Humboldt Fellow in April-June 2001, and completed during his stay at the Atilim University, Ankara in the academic year 2001-2002. He would like to thank these institutions for hospitality and the Alexander von Humboldt-Stiftung for financial support. He is indebted to Sorin Dascalescu and Serban Raianu for helpful discussions on various topics of Hopf algebras
SOME EXAMPLES IN COGALOIS THEORY WITH APPLICATIONS TO ELEMENTARY FIELD ARITHMETIC
No full text The aim of this paper is to provide some examples in Cogalois Theory showing that the property of a field extension to be radical (resp. Kneser, or Cogalois) is not transitive and is not inherited by subextensions. Our examples refer especially to extensions of type [Formula: see text]. We also effectively calculate the Cogalois groups of these extensions. A series of applications to elementary arithmetic of fields, like: • for what n, d ∈ ℕ* is [Formula: see text] a sum of radicals of positive rational numbers • when is [Formula: see text] a finite sum of monomials of form [Formula: see text], where r, j1,…, jr ∈ ℕ*, c ∈ ℚ*, and [Formula: see text] are also presented. </jats:p
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