Mapping property

2019 ◽  
Vol 105 (4) ◽  
pp. 508-526
Author(s):  
Anjali Vats
Keyword(s):  
Mapping Property

Localization in Algebra

2020 ◽  
pp. 189-196
Author(s):  
Loring W. Tu
Keyword(s):  
Closed Subset ◽  
Mapping Property ◽  
Direct Sum

This chapter provides a digression concerning the all-important technique of localization in algebra. Localization generally means formally inverting a multiplicatively closed subset in a ring. However, the chapter focuses on the particular case of inverting all nonnegative powers of a variable u in an ℝ[u]-module. Localization of an ℝ[u]-module with respect to a variable u kills the torsion elements and preserves exactness. The chapter then looks at the proposition that localization preserves the direct sum. The simplest proof for this proposition is probably one that uses the universal mapping property of the direct sum. The chapter also considers antiderivations under localization.

Positivity conditions for polynomials

1994 ◽  
Vol 14 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Valerio De Angelis
Keyword(s):  
Entropy Function ◽  
Legendre Transformation ◽  
Mapping Property ◽  
Laurent Polynomials ◽  
Positivity Condition ◽  
Several Variables

AbstractWe study several notions of positivity for a class of real-valued functions of several variables that includes the Laurent polynomials. We show that Handelman's positivity condition is characterized by boundedness of the associated Legendre transformation, or boundedness of the entropy function, while another notion of positivity here introduced characterizes the mapping property of the Legendre transformation derived by Marcus and Tuncel for beta functions. Several examples are given to distinguish the various notions of positivity.

On the structure of generalized Albanese varieties

1992 ◽  
Vol 111 (2) ◽  
pp. 267-272
Author(s):  
Hurit nsiper
Keyword(s):  
Algebraic Group ◽  
Class Group ◽  
Effective Divisor ◽  
Closed Field ◽  
Projective Surface ◽  
Mapping Property ◽  
Rational Map ◽  
Algebraically Closed Field ◽  
Albanese Map ◽  
Albanese Variety

Given a smooth projective surface X over an algebraically closed field k and a modulus (an effective divisor) m on X, one defines the idle class group Cm(X) of X with modulus m (see 1, chapter III, section 4). The corresponding generalized Albanese variety Gum and the generalized Albanese map um:X|m|Gum have the following universal mapping property (2): if :XG is a rational map into a commutative algebraic group which induces a homomorphism Cm(X)G(k) (1, chapter III, proposition 1), then factors uniquely through um.

A Universal Mapping Property for a Lattice Completion

1976 ◽  
Vol 6 (1) ◽  
pp. 81-84 ◽  
Author(s):  
Alan A. Bishop
Keyword(s):  
Mapping Property

scholarly journals The spectral mapping property for p–multiplier operators on compact abelian groups

2005 ◽  
Vol 78 (3) ◽  
pp. 423-428 ◽  
Author(s):  
Werner J. Ricker
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Dual Group ◽  
Compact Set ◽  
Mapping Property ◽  
Spectral Mapping ◽  
Multiplier Operator ◽  
Algebraic Properties ◽  
Compact Abelian Groups ◽  
Multiplier Operators

AbstractLet G be a compact abelian group and 1< p < ∞. It is known that the spectrum σ (Tψ) of a Fourier p–multiplier operator Tψ acting in Lp(G), may fail to coincide with its natural spectrum ψ(Г) if p ≠ 2; here Γ is the dual group to G and the bar denotes closure in C. Criteria are presented, based on geometric, topological and/or algebraic properties of the compact set σ(Tψ), which are sufficient to ensure that the equality σ(Tψ) = ψ(Г)holds.

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