On the Polynomial Ring over a Mori Domain
Valentina Barucci (1988)
Publications du Département de mathématiques (Lyon)
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Valentina Barucci (1988)
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Robert Gilmer, William Heinzer (1994)
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Christel Rotthaus (1983)
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Mitsuhiro Miyazaki (1989)
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Klaus Langmann (1976)
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Putcha, Mohan.S., Yaqub, Adil (1979)
International Journal of Mathematics and Mathematical Sciences
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Jean Marot (1980/81)
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Putcha, Mohan S., Yaqub, Adil (1981)
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Al-Ezeh, H. (1988)
International Journal of Mathematics and Mathematical Sciences
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Noboru Endou, Kazuhisa Nakasho, Yasunari Shidama (2015)
Formalized Mathematics
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In this article, semiring and semialgebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semiring of sets has already been formalized in [13], that is, strictly speaking, a definition of a quasi semiring of sets suggested in the last few decades [15]. We adopt a classical definition of a semiring of sets here to avoid such a confusion. Ring of sets and algebra of sets have been formalized as non empty preboolean set [23] and field of subsets...
Yau, Donald (2004)
International Journal of Mathematics and Mathematical Sciences
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H.E.A. Campbell, I.P. Hughes (1996)
Mathematische Annalen
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Piotr Pragacz, Jan Ratajski (1993)
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Sanghare, Mamadou (1997)
International Journal of Mathematics and Mathematical Sciences
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Yuichi Futa, Yasunari Shidama (2017)
Formalized Mathematics
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In this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. ℤ-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and Lovász) [5] base reduction algorithm and cryptographic systems [6, 2].