Notes on the linearity defect and applications
نویسندگان
چکیده
منابع مشابه
Lecture Notes on Linearity (Group Homomorphism) Testing
Let G and H be two groups. For simplicity, we denote by + the group operation in each of these groups. A function f : G → H is called a (group) homomorphism if for every x, y ∈ G it holds that f(x+ y) = f(x) + f(y). One important special case of interest is when H is a finite field and G is a vector space over this field; that is, G = H for some natural number m. In this case, a homomorphism f ...
متن کاملOn the Linearity Defect of the Residue Field
Given a commutative Noetherian local ring R, the linearity defect of a finitely generated R-module M , denoted ldR(M), is an invariant that measures how far M and its syzygies are from having a linear resolution. Motivated by a positive known answer in the graded case, we study the question of whether ldR(k) < ∞ implies ldR(k) = 0. We give answers in special cases, and we discuss several interp...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2015
ISSN: 0019-2082
DOI: 10.1215/ijm/1475266401