Researcher:
Albu, Toma

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Toma

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Albu

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Albu, Toma

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2004 - 20076

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Researcher Of Publications: search.filters.isAuthorOfPublication.ab3cf8c2-92c0-40c2-bf02-d286fcde8188

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    Modular QFD lattices with applications to grothendieck categories and torsion theories
    (World Scientific Publishing, 2004) Iosif, Mihai; Teply, Mark L.; Department of Mathematics; Albu, Toma; Faculty Member; Department of Mathematics; College of Sciences; N/A
    A modular lattice L with 0 and 1 is called quotient finite dimensional (QFD) if [x, 1] has no infinite independent set for any x is an element of L. We extend some results about QFD modules to upper continuous modular lattices by using Lemonnier's Lemma. One result says that QFD for a compactly generated lattice L is equivalent to Condition (C): for every m is an element of L, there exists a compact element t of L such that t is an element of [0, m] and [t, m[ has no maximal element. If L is not compactly generated, then QFD and (C) separate into two distinct conditions, which are analyzed and characterized for upper continuous modular lattices. We also extend to upper continuous modular lattices some characterizations of QFD modules with Gabriel dimension. Applications of these results are given to Grothendieck categories and module categories equipped with a torsion theory.
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    Dual krull dimension and quotient finite dimensionality
    (Elsevier, 2005) Iosif, Mihai; Teply, Mark L.; Department of Mathematics; Albu, Toma; Faculty Member; Department of Mathematics; College of Sciences; N/A
    A modular lattice L with 0 and 1 is called quotient finite dimensional (QFD) if [x, 1] has no infinite independent set for any x epsilon L. We characterize upper continuous modular lattices L that have dual Krull dimension k(0) (L) less than or equal to alpha, 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. (C) 2004 Elsevier Inc. All rights reserved.
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    An Abstract Cogalois Theory for profinite groups
    (Elsevier, 2005) Basarab, EA; Department of Mathematics; Albu, Toma; Faculty Member; Department of Mathematics; College of Sciences; N/A
    The aim of this paper is to develop an abstract group theoretic framework for the Cogalois Theory of field extensions. (c) 2005 Elsevier B.V. All rights reserved.
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    Field theoretic cogalois theory via abstract cogalois theory
    (Elsevier, 2007) Department of Mathematics; Albu, Toma; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Cogalois Theory for arbitrary profinite groups was initiated by T. Albu and 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. (c) 2005 Elsevier B.V. All rights reserved.
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    Toward an abstract cogalois theory (I): Kneser and Cogalois groups of cocycles
    (The Institute of Mathematics of the Romanian Academy, 2004) Basarab, Şerban A.; Department of Mathematics; Albu, Toma; Faculty Member; Department of Mathematics; College of Sciences
    This is the first part of a series of papers which aim to develop an abstract group theoretic framework for the Cogalois Theory of field extensions.
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    Field Theoretic Cogalois Theory via Abstract Cogalois Theory
    (Elsevier, 2007) Department of Mathematics; Albu, Toma; Faculty Member; Department of Mathematics; College of Sciences
    Cogalois Theory for arbitrary profinite groups was initiated by T. Albu and S¸.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.