Free modules over hjelmslev rings in which not every maximal linearly independent subset is a basis

1992 ◽  
Vol 45 (1-2) ◽  
pp. 105-113 ◽  
Author(s):  
Alexander Kreuzer
Keyword(s):  
Independent Subset ◽  
Linearly Independent ◽  
Free Modules

scholarly journals Central elements of the Jennings basis and certain Morita invariants

2019 ◽  
Vol 19 (08) ◽  
pp. 2050160 ◽  
Author(s):  
Taro Sakurai
Keyword(s):  
Group Algebra ◽  
Positive Characteristic ◽  
Finite Dimensional Algebra ◽  
Independent Subset ◽  
Dimensional Algebra ◽  
Ideal Formula ◽  
Finite Dimensional ◽  
Linearly Independent ◽  
Morita Invariant ◽  
Central Elements

From Morita theoretic viewpoint, computing Morita invariants is important. We prove that the intersection of the center and the [Formula: see text]th (right) socle [Formula: see text] of a finite-dimensional algebra [Formula: see text] is a Morita invariant; this is a generalization of important Morita invariants — the center [Formula: see text] and the Reynolds ideal [Formula: see text]. As an example, we also studied [Formula: see text] for the group algebra FG of a finite [Formula: see text]-group [Formula: see text] over a field [Formula: see text] of positive characteristic [Formula: see text]. Such an algebra has a basis along the socle filtration, known as the Jennings basis. We prove certain elements of the Jennings basis are central and hence form a linearly independent subset of [Formula: see text]. In fact, such elements form a basis of [Formula: see text] for every integer [Formula: see text] if [Formula: see text] is powerful. As a corollary we have [Formula: see text] if [Formula: see text] is powerful.

Linear Independence of Logarithms of Cyclotomic Numbers and a Conjecture of Livingston

2019 ◽  
Vol 63 (1) ◽  
pp. 31-45
Author(s):  
Tapas Chatterjee ◽  
Sonika Dhillon
Keyword(s):  
Linear Independence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sine Function ◽  
Independent Subset ◽  
Linearly Independent ◽  
Cyclotomic Numbers ◽  
Necessary And Sufficient ◽  
Trigonometric Identities ◽  
Rational Arguments

AbstractIn 1965, A. Livingston conjectured the $\overline{\mathbb{Q}}$-linear independence of logarithms of values of the sine function at rational arguments. In 2016, S. Pathak disproved the conjecture. In this article, we give a new proof of Livingston’s conjecture using some fundamental trigonometric identities. Moreover, we show that a stronger version of her theorem is true. In fact, we modify this conjecture by introducing a co-primality condition, and in that case we provide the necessary and sufficient conditions for the conjecture to be true. Finally, we identify a maximal linearly independent subset of the numbers considered in Livingston’s conjecture.

Productly linearly independent sequences

2015 ◽  
Vol 52 (3) ◽  
pp. 350-370
Author(s):  
Jaroslav Hančl ◽  
Katarína Korčeková ◽  
Lukáš Novotný
Keyword(s):  
Rational Numbers ◽  
Infinite Products ◽  
Linearly Independent ◽  
New Concepts ◽  
Infinite Sequences

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

Boundary Value Problems of Electroelasticity with Concentrated Singularities

1994 ◽  
Vol 1 (5) ◽  
pp. 459-467
Author(s):  
T. Buchukuri ◽  
D. Yanakidi
Keyword(s):  
Singular Point ◽  
Boundary Value Problems ◽  
Power Function ◽  
Boundary Value ◽  
Linearly Independent

Abstract We investigate the solutions of boundary value problems of linear electroelasticity, having growth as a power function in the neighbourhood of infinity or in the neighbourhood of an isolated singular point. The number of linearly independent solutions of this type is established for homogeneous boundary value problems.

scholarly journals Modular invariant models of leptons at level 7

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Gui-Jun Ding ◽  
Stephen F. King ◽  
Cai-Chang Li ◽  
Ye-Ling Zhou
Keyword(s):  
Modular Forms ◽  
Galois Field ◽  
Special Linear Group ◽  
Type I ◽  
Time Level ◽  
Projective Special Linear Group ◽  
Modular Invariant ◽  
Seesaw Mechanism ◽  
Linearly Independent ◽  
First Time

Abstract We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms. The latter are decomposed into irreducible multiplets of the finite modular group Γ7, which is isomorphic to PSL(2, Z7), the projective special linear group of two dimensional matrices over the finite Galois field of seven elements, containing 168 elements, sometimes written as PSL2(7) or Σ(168). At weight 2, there are 26 linearly independent modular forms, organised into a triplet, a septet and two octets of Γ7. A full list of modular forms up to weight 8 are provided. Assuming the absence of flavons, the simplest modular-invariant models based on Γ7 are constructed, in which neutrinos gain masses via either the Weinberg operator or the type-I seesaw mechanism, and their predictions compared to experiment.

scholarly journals On independence of iterated Whitehead doubles in the knot concordance group

2018 ◽  
Vol 27 (01) ◽  
pp. 1850003
Author(s):  
Kyungbae Park
Keyword(s):  
Correction Term ◽  
Khovanov Homology ◽  
Floer Theory ◽  
Knot Concordance ◽  
Torus Knot ◽  
Linearly Independent ◽  
Heegaard Floer

Let [Formula: see text] be the positively clasped untwisted Whitehead double of a knot [Formula: see text], and [Formula: see text] be the [Formula: see text] torus knot. We show that [Formula: see text] and [Formula: see text] are linearly independent in the smooth knot concordance group [Formula: see text] for each [Formula: see text]. Further, [Formula: see text] and [Formula: see text] generate a [Formula: see text] summand in the subgroup of [Formula: see text] generated by topologically slice knots. We use the concordance invariant [Formula: see text] of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the [Formula: see text]-invariant of knot Floer theory and the [Formula: see text]-invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of [Formula: see text] for any [Formula: see text] generalizing a result for [Formula: see text] of Hedden, Kim and Livingston.

Sign in / Sign up

Export Citation Format

Share Document