On P-extending modules.
Kamal, M.A., Elmnophy, O.A. (2005)
Acta Mathematica Universitatis Comenianae. New Series
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Kamal, M.A., Elmnophy, O.A. (2005)
Acta Mathematica Universitatis Comenianae. New Series
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Oneto R., Ángel V. (1996)
Divulgaciones Matemáticas
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H. Ansari-Toroghy, F. Farshadifar (2008)
Archivum Mathematicum
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Let be a ring with an identity (not necessarily commutative) and let be a left -module. This paper deals with multiplication and comultiplication left -modules having right -module structures.
Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2012)
Formalized Mathematics
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In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].
Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2012)
Formalized Mathematics
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In this article we formalize a quotient module of Z-module and a vector space constructed by the quotient module. We formally prove that for a Z-module V and a prime number p, a quotient module V/pV has the structure of a vector space over Fp. Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattices [14]. Some theorems in this article are described by translating theorems in [20] and [19] into theorems...
Wisbauer, Robert, Yousif, Mohamed F., Zhou, Yiqiang (2002)
Beiträge zur Algebra und Geometrie
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Li, Linlin, Wei, Jiaqun (2008)
Matematichki Vesnik
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Markus Schmidmeier (1998)
Colloquium Mathematicae
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Andrzej Borowiec, Vladislav Kharchenko, Zbigniew Oziewicz (1997)
Banach Center Publications
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The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and Zumino [1990] and that in this language results are in a natural context, are easier to describe and handle. As a by-product we obtain intrinsic, coordinate-free and basis-independent generalization of the first order noncommutative differential calculi with partial derivatives.