Extensions of a ring by a ring with a bimodule structure
Abstract: A type of ring extension is considered that was introduced by J. Szendrei and generalizes many familiar examples, including the complex extension of the real field. We give a method for constructing a large class of examples of this type of extension, and show that for some rings all possible examples are obtained by this method. An abstract characterization of the extension is also given, among rings defined on the set product of two given rings.
-  C. W. Kohls and L. J. Lardy, On extensions and bimultiplication algebras of algebras, Arch. Math. (Basel) 20 (1969), 365–372. MR 0251056, https://doi.org/10.1007/BF01899591
-  C. W. Kohls and L. J. Lardy, Some ring extensions with matrix representations, Pacific J. Math. 26 (1968), 341–348. MR 0237572
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Keywords: Ring extension, bimultiplication ring, biadditive function, bimodule, commutative ring with identity, integral domain
Article copyright: © Copyright 1970 American Mathematical Society