algebra module
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2019 ◽  
Vol 26 (02) ◽  
pp. 195-230
Author(s):  
Zhuo Chen ◽  
Honglei Lang ◽  
Maosong Xiang

The subject of this paper is strongly homotopy (SH) Lie algebras, also known as L∞-algebras. We extract an intrinsic character, the Atiyah class, which measures the nontriviality of an SH Lie algebra A when it is extended to L. In fact, with such an SH Lie pair (L, A) and any A-module E, there is associated a canonical cohomology class, the Atiyah class [αE], which generalizes the earlier known Atiyah classes out of Lie algebra pairs. We show that the Atiyah class [αL/A] induces a graded Lie algebra structure on [Formula: see text], and the Atiyah class [αE] of any A-module E induces a Lie algebra module structure on [Formula: see text]. Moreover, Atiyah classes are invariant under gauge equivalent A-compatible infinitesimal deformations of L.


2019 ◽  
Vol 19 (04) ◽  
pp. 2050064 ◽  
Author(s):  
T. Kurbanbaev ◽  
R. Turdibaev

We study complex finite-dimensional Leibniz algebra bimodule over [Formula: see text] that as a Lie algebra module is split into a direct sum of two simple [Formula: see text]-modules. We prove that in this case there are only two nonsplit Leibniz [Formula: see text]-bimodules and we describe the actions.


2019 ◽  
Vol 19 (01) ◽  
pp. 2050019 ◽  
Author(s):  
Hashem Bordbar ◽  
Michal Novák ◽  
Irina Cristea

In this paper, we initiate the study of the notion of support of a hypermodule over a Krasner hyperring, providing several connections with the annihilator of such hypermodules. We concentrate on the similarities/differences between these concepts and the analogous ones from classical algebra (module theory). After defining and characterizing the support of a hypermodule (and in particular of a finitely generated hypermodule), by using the notion of length of a hypermodule, we determine the support of a quotient hypermodule containing only one maximal hyperideal.


2019 ◽  
Vol 1155 ◽  
pp. 012080 ◽  
Author(s):  
K Mawardi ◽  
E S Dewi ◽  
S Asmah ◽  
T N Pratiwi ◽  
U I Sari ◽  
...  

2018 ◽  
Vol 15 (1) ◽  
pp. 102-105 ◽  
Author(s):  
Baghdad Science Journal

The concept of fully pseudo stable Banach Algebra-module (Banach A-module) which is the generalization of fully stable Banach A-module has been introduced. In this paper we study some properties of fully stable Banach A-module and another characterization of fully pseudo stable Banach A-module has been given.


Author(s):  
Cut Intan Salasiyah

This study aims to produce Linear Algebra module for mathematics education students. This type of research is research development (R & D) with Plomp development model. The Plomp development model consists of five phases, namely: initial investigation phase, design phase, realization/construction phase, test phase, evaluation, and revision, and implementation phase. This research was conducted on students of mathematics education program of FKIP Samudra State University. Instruments used are in the form of validation sheet, test sheet and the questionnaire. The results showed that the Linear Algebra module that has been developed already met the aspects of good module quality, namely: the feasibility test module, Linear Algebra module that has been developed is valid based on the expert assessment; effectiveness test, where Linear Algebra module has an impact on the level of mastery and understanding of students on good criteria; test of practicality, where the result of questionnaire of practicality analysis shows that the module that has been developed can be implemented and used by the students.


2015 ◽  
Vol 62 (1) ◽  
pp. 31-35
Author(s):  
Khondokar M Ahmed ◽  
Saraban Tahora

In the present paper some aspects of tensor algebra, tensor product, exterior algebra, symmetric algebra, module of section, graded algebra, vector subbundle are studied. A Theorem 1.32. is established by using sections and fibrewise orthogonal sections of an application of Gran-Schmidt. DOI: http://dx.doi.org/10.3329/dujs.v62i1.21957 Dhaka Univ. J. Sci. 62(1): 31-35, 2014 (January)


2013 ◽  
Vol 247 ◽  
pp. 192-265 ◽  
Author(s):  
Alexei Davydov ◽  
Ingo Runkel
Keyword(s):  

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