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| Ultima descărcare din IBN: 2023-03-28 21:03 |
 SM ISO690:2012CIMPOEAS, Mircea. On the algebraic properties of the ring of Dirichlet convolutions. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, pp. 89-90. ISBN 978-9975-76-247-2. |
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| Conference on Applied and Industrial Mathematics Ediţia a 26-a, 2018 |
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Conferința "Conference on Applied and Industrial Mathematics" Iași, România, Romania, 20-22 septembrie 2018 | ||||||
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| Rezumat | ||||||
Let (Г; _) be a commutative monoid of _nite type and let R be a commutative ring with unity.In the set of functions de_ned on Г with values in R, F(Г;R) := f_ : Г ! Rg, we consider the operations (_ + _)(n) := _(n) + _(n); (8)n 2 Г and (_ _ _)(n) := X ab=n _(a)_(b); (8)n 2 Г: It is well known that (F(Г;R);+; _) is a commutative ring with unity, see for instance [3]. Let Mbe a R-module. Let F(Г;M) := ff : Г ! Mg. For any f; g 2 F(Г;M) and _ 2 F(Г;R), we define:(f + g)(n) := f(n) + g(n); (8)n 2 Г and (_ _ f)(n) := X ab=n _(a)f(b); (8)n 2 Г: We show that F(Г;M) has a natural structure of a F(Г;R)-module and we discuss certain properties of the functor M 7! (Г;M). Given a morphism of monoids L : (Г; _) ! (M; +), we show that the induced map _L;M : F(Г;M) ! FL(Г;M); _L;M(f)(n) := L(n)f(n) is a morphism of F(Г;R)-modules. |
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