Generalized Malcev-Neumann Series Modules with the Beachy-Blair Condition. (15th March 2015)

• Record Type: Journal Article
• Authors: Farahat, Mohamed A.
• Other Names: Kelarev Andrei V. Academic Editor.
• Is Part Of: Algebra. Volume 2015(2015)
• Publication Date: 2015-03-15
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2015/595274
• Languages: English
• ISSNs: 2314-4106

Abstract

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 ) ) .