Generalized Malcev-Neumann Series Modules with the Beachy-Blair Condition. (15th March 2015) - Farahat, Mohamed A.
Abstract : We introduce a new class of extension rings called the generalized Malcev-Neumann series ring R ( ( S ; σ ; τ ) ) with coefficients in a ringR and exponents in a strictly ordered monoidS which extends the usual construction of Malcev-Neumann series rings. Ouyang et al. in 2014 introduced the modules with the Beachy-Blair condition as follows: A rightR -module satisfies the right Beachy-Blair condition if each of its faithful submodules is cofaithful. In this paper, we study the relationship between the right Beachy-Blair condition of a rightR -moduleM R and its Malcev-Neumann series module extensionM S R ( ( S ; σ ; τ ) ) .