scholarly journals Reconstructing the base field from imaginary multiplicative chaos

2021 ◽  
Author(s):  
Juhan Aru ◽  
Janne Junnila
Keyword(s):  
Base Field

Regular Hom-algebras admitting a multiplicative basis

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonio J. Calderón Martín
Keyword(s):  
Arbitrary Dimension ◽  
Base Field ◽  
Direct Sum ◽  
Multiplicative Basis ◽  
Arbitrary Base ◽  
The Family

AbstractLet {({\mathfrak{H}},\mu,\alpha)} be a regular Hom-algebra of arbitrary dimension and over an arbitrary base field {{\mathbb{F}}}. A basis {{\mathcal{B}}=\{e_{i}\}_{i\in I}} of {{\mathfrak{H}}} is called multiplicative if for any {i,j\in I}, we have that {\mu(e_{i},e_{j})\in{\mathbb{F}}e_{k}} and {\alpha(e_{i})\in{\mathbb{F}}e_{p}} for some {k,p\in I}. We show that if {{\mathfrak{H}}} admits a multiplicative basis, then it decomposes as the direct sum {{\mathfrak{H}}=\bigoplus_{r}{{\mathfrak{I}}}_{r}} of well-described ideals admitting each one a multiplicative basis. Also, the minimality of {{\mathfrak{H}}} is characterized in terms of the multiplicative basis and it is shown that, in case {{\mathcal{B}}}, in addition, it is a basis of division, then the above direct sum is composed by means of the family of its minimal ideals, each one admitting a multiplicative basis of division.

scholarly journals Differential Modules on p-Adic Polyannuli—Erratum

2010 ◽  
Vol 9 (3) ◽  
pp. 669-671 ◽  
Author(s):  
Kiran S. Kedlaya ◽  
Liang Xiao
Keyword(s):  
Base Field ◽  
Convergence Theorems ◽  
Differential Modules

The statement of Theorem 2.7.6 in the indicated paper is incorrect. For instance, if m = 0 (i.e., the base field K contains no additional derivations), it is inconsistent with Theorem 2.7.4 due to the distinction between intrinsic and extrinsic generic radii of convergence. Theorems 2.7.12 and 2.7.13 are incorrect for similar reasons.

scholarly journals FRAMED CORRESPONDENCES AND THE MILNOR–WITT -THEORY

2016 ◽  
Vol 17 (4) ◽  
pp. 823-852 ◽  
Author(s):  
Alexander Neshitov
Keyword(s):  
Characteristic Zero ◽  
Triangulated Category ◽  
Algebraic Varieties ◽  
Base Field ◽  
Witt Theory

Given a field $k$ of characteristic zero and $n\geqslant 0$, we prove that $H_{0}(\mathbb{Z}F(\unicode[STIX]{x1D6E5}_{k}^{\bullet },\mathbb{G}_{m}^{\wedge n}))=K_{n}^{MW}(k)$, where $\mathbb{Z}F_{\ast }(k)$ is the category of linear framed correspondences of algebraic $k$-varieties, introduced by Garkusha and Panin [The triangulated category of linear framed motives $DM_{fr}^{eff}(k)$, in preparation] (see [Garkusha and Panin, Framed motives of algebraic varieties (after V. Voevodsky), Preprint, 2014, arXiv:1409.4372], § 7 as well), and $K_{\ast }^{MW}(k)$ is the Milnor–Witt $K$-theory of the base field $k$.

scholarly journals The Academic Knowledge Management Model of Small Schools in Thailand

2015 ◽  
Vol 8 (11) ◽  
pp. 266
Author(s):  
Chamnan Tumtuma ◽  
Chalard Chantarasombat ◽  
Theerawat Yeamsang
Keyword(s):  
Knowledge Management ◽  
Research And Development ◽  
Field Study ◽  
Qualitative Data ◽  
Small Schools ◽  
Group Discussion ◽  
Management Model ◽  
Base Field ◽  
Academic Knowledge ◽  
Participatory Workshop

<p class="apa">The Academic Knowledge Management Model of Small Schools in Thailand was created by research and development. The quantitative and qualitative data were collected via the following steps: a participatory workshop meeting, the formation of a team according to knowledge base, field study, brainstorming, group discussion, activities carried out according to knowledge, summarizing and revising the operation, organizing an exhibition to show the work results, and the creation of a website. The results showed that the subjects had knowledge of how to manage knowledge, became more academically capable, and were satisfied with knowledge management at the highest level.</p>

Behaviour of krull dimension under extension of the base field

1991 ◽  
Vol 19 (1) ◽  
pp. 143-156
Author(s):  
Timothy J. Hodges ◽  
Kyunghee Kim ◽  
Richard Resco
Keyword(s):  
Krull Dimension ◽  
Base Field

scholarly journals On the Structure of Graded Leibniz Algebras

2015 ◽  
Vol 22 (01) ◽  
pp. 83-96 ◽  
Author(s):  
Antonio J. Calderón Martín ◽  
José M. Sánchez Delgado
Keyword(s):  
Arbitrary Dimension ◽  
Unit Element ◽  
Homogeneous Component ◽  
Maximal Length ◽  
Base Field ◽  
Leibniz Algebras ◽  
Arbitrary Base

We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field 𝕂. We show that any of such algebras 𝔏 with a symmetric G-support is of the form [Formula: see text] with U a subspace of 𝔏1, the homogeneous component associated to the unit element 1 in G, and any Ij a well described graded ideal of 𝔏, satisfying [Ij, Ik]=0 if j ≠ k. In the case of 𝔏 being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.

Double Derivations of n-Lie Superalgebras

2018 ◽  
Vol 25 (01) ◽  
pp. 161-180
Author(s):  
Bing Sun ◽  
Liangyun Chen ◽  
Xin Zhou
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
General Linear ◽  
Base Field ◽  
Inner Derivation ◽  
Derivation Algebra ◽  
General Linear Lie Superalgebra

Let 𝔤 be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(𝔤). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(𝔤) and the inner derivation algebra ad(𝔤) is an ideal of [Formula: see text]. We also show that if 𝔤 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(𝔤) in [Formula: see text] is trivial. Finally, we give that for every perfect n-Lie superalgebra 𝔤, the triple derivations of the derivation algebra Der(𝔤) are exactly the derivations of Der(𝔤).

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