faithful module
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2017 ◽  
Vol 81 (1) ◽  
pp. 91-98 ◽  
Author(s):  
O A Pikhtilkova ◽  
S A Pikhtilkov


2014 ◽  
Vol 57 (2) ◽  
pp. 231-239 ◽  
Author(s):  
J. Bagherian

AbstractIn this paper we show that every module of a table algebra can be considered as a faithful module of some quotient table algebra. Also we prove that every faithful module of a table algebra determines a closed subset that is a cyclic group. As a main result we give some information about multiplicities of characters in table algebras.



1984 ◽  
Vol 36 (2) ◽  
pp. 193-205 ◽  
Author(s):  
Soumaya Makdissi Khuri

A basic tool in the usual presentation of the Morita theorems is the correspondence theorem for projective modules. Let RM be a left R-module and B = HomR(M, M). When M is a progenerator, there is a close connection (in fact a lattice isomorphism) between left R-submodules of M and left ideals of B, which can be applied to the solution of problems such as characterizing when the endomorphism ring of a finitely generated projective faithful module is simple or right Noetherian. More generally, Faith proved that this connection can be retained in suitably modified form when M is just a generator in R-mod ([4], [2], [3]). In this form the correspondence theorem can be applied to show, e.g., that, when RM is a generator, then (a): RM is finite-dimensional if and only if B is a left finite-dimensional ring and in this case d(RM) = d(BB), and (b): If RM is nonsingular then B is a left nonsingular ring ([6]).



1968 ◽  
Vol 31 ◽  
pp. 173-183 ◽  
Author(s):  
Bruno J. Mueller

QF-3 algebras R are classified according to their second commutator algebras R′ with respect to the minimal faithful module, which satisfy dom.dim. R′ ≧ 2. The class C(S) of all QF-3 algebras whose second commutator is S, contains besides S only algebras R with dom.dim. R = 1. C(S) contains a unique (up to isomorphism) minimal algebra which can be represented as a subalgebra S0 of S describable in terms of the structure of S, and C(S) consists just of the algebras S0 ⊂ R ⊂ S (up to isomorphism).



1957 ◽  
Vol 9 ◽  
pp. 60-67
Author(s):  
Hans Schneider

Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteristic polynomial of a on V which does not involve determinants.



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