Modular representations of Loewy length two.
Charkani, M.E., Bouhamidi, S. (2003)
International Journal of Mathematics and Mathematical Sciences
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Charkani, M.E., Bouhamidi, S. (2003)
International Journal of Mathematics and Mathematical Sciences
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Yuqun Chen, Yongshan Chen, Chanyan Zhong (2010)
Czechoslovak Mathematical Journal
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We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the...
Philip Olin (1971)
Fundamenta Mathematicae
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Wang, Yongduo (2005)
International Journal of Mathematics and Mathematical Sciences
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Gabriella D'Este, Dieter Happel (1990)
Rendiconti del Seminario Matematico della Università di Padova
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Ladislav Bican (1972)
Czechoslovak Mathematical Journal
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Ameri, Reza (2004)
International Journal of Mathematics and Mathematical Sciences
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Enochs, Edgar E., López-Ramos, J.A., Torrecillas, B. (2002)
International Journal of Mathematics and Mathematical Sciences
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Kamal, Mahmoud Ahmed (1994)
International Journal of Mathematics and Mathematical Sciences
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Yuichi Futa, Yasunari Shidama (2016)
Formalized Mathematics
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In this article, we formalize the definition of divisible ℤ-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible ℤ-modules are not finitely-generated.We introduce a divisible ℤ-module, equivalent to a vector space of a torsion-free ℤ-module with a coefficient ring ℚ. ℤ-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8]. ...