ADS modules

We study the class of ADS rings and modules introduced by Fuchs. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R is ADS as a right R-module must be either right self-injective or indecomposable as a right R-module. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.Comment: 7 page

Saudi-KAU Coupled Global Climate Model: Description and Performance

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Invariance and parallel sums

© 2020 © The Author(s). In this paper, the notions of invariance and parallel sums as defined by Anderson and Duffin for matrices [Series and parallel addition of matrices, J. Math. Anal. Appl. 26 (1969) 576-594] are generalized to von Neumann regular rings

Matrix wreath products of algebras and embedding theorems

© 2019 American Mathematical Society. We introduce a new construction of matrix wreath products of algebras that is similar to wreath products of groups. We then use it to prove embedding theorems for Jacobson radical, nil, and primitive algebras. In §6, we construct finitely generated nil algebras of arbitrary Gelfand-Kirillov dimension ≥ 8 over a countable field which answers a question from [New trends in noncommutative algebra, Amer. Math. Soc., Providence, RI, 2012, pp. 41-52]