Papers by Giulia Maria Cattaneo
Il libro potrà essere utile a studenti e/oa studiosi, sia di discipline teoriche, come i matemati... more Il libro potrà essere utile a studenti e/oa studiosi, sia di discipline teoriche, come i matematici puri, che applicative come fisici, informatici o ingegneri, che intendano avvicinarsi alla crittografia. Costoro troveranno nel libro un approccio elementare, pur avendo il testo l´ ...
C6.12. Write a program that decides whether a given integer m is an h-tuple residue modulo n, whe... more C6.12. Write a program that decides whether a given integer m is an h-tuple residue modulo n, when a primitive root modulo n exists. C6.13. Write a program that factors an integer using Fermat factorisation method described in § 6.4.2. C6.14. Write a program that factors an integer using the method of factor bases described in § 6.4.3. C6.15. Write a program that factors an integer using the improved method of factor bases described in § 6.4.4. C6.16. Write a program that factors an integer using the quadratic sieve method described in § 6.4.5. C6.17. Write a program that factors an integer using the ρ method as described in § 6.4.6 or in § 6.4.7.
Elementary Number Theory, Cryptography and Codes, 2009
Communications in Algebra, 1984
... ouickly. Prelimi~aries: We assume that our algebras are over a field of characteris-tic not 2... more ... ouickly. Prelimi~aries: We assume that our algebras are over a field of characteris-tic not 2 and not 3 . This paper studies identities of the ... submodule. The power of Theorem 1 lies in the fact that when F is of characteristic # 2 and f 3, then the grouo ring A is Page 6. 2354 ...
Polynomial Identities And Combinatorial Methods, 2003
Maria Welleda Baldoni Ciro Ciliberto Giulia Maria Piacentini Cattaneo Università di Roma - Tor Ve... more Maria Welleda Baldoni Ciro Ciliberto Giulia Maria Piacentini Cattaneo Università di Roma - Tor Vergata Dipartimento di Matematica Via della Ricerca Scientifica, 1 00133 Roma Italy [email protected] [email protected] [email protected] Translator: ...
Transactions of the American Mathematical Society, 1977
R). Such algebras include (-1, 1) algebras, Lie algebras, and, as we show, a large number of asso... more R). Such algebras include (-1, 1) algebras, Lie algebras, and, as we show, a large number of associator dependent algebras. An alternator is an associator of the type (a, a, b), {a, b, a), (f>, a, a). We next study algebras where the additive span of all alternators is an ideal. These include all algebras where I = {R, R, R) as well as alternative algebras. The last section deals with prime, right alternative, alternator ideal algebras satisfying an identity of the form [x, (x, x, a)] = y(x, x, [x, a]) for fixed y. With two exceptions, if this algebra has an idempotent e such that (e, e, R) = 0, then the algebra is alternative. All our work deals with algebras with an identity element over a field of characteristic prime to 6. All our containment relations are given by identities.
Transactions of the American Mathematical Society, 1975
We study nonassociative rings R satisfying the conditions (1) (ab, c, d) + (a, b, [c, d]) = a(b, ... more We study nonassociative rings R satisfying the conditions (1) (ab, c, d) + (a, b, [c, d]) = a(b, c, d) + (a, c, d)b for all a, b, c, d e R, and (2) (x, x, x) = 0 for all x S. R. We furthermore assume weakly characteristic not 2 and weakly characteristic not 3. As both (1) and (2) are consequences of the right alternative law, our rings are generalizations of right alternative rings. We show that rings satisfying (1) and (2) which are simple and have an idempotent + 0, # 1, are right alternative rings. We show by example that (x, e, e) may be nonzero. In general, R = R' + (R, e, e) (additive direct sum) where R' is a subring and (R, e, e) is a nilpotent ideal which commutes elementwise with R. We examine R' under the added assumption of Lie admissibility: (3) (a, b, c) + (Jb, c, a) + (c, a, b) = 0 for all a, b, cEJi, We generate the Peirce decomposition. If R' has no trivial ideals contained in its center, the table for the multiplication of the summands is associative, and the nucleus of R' contains R'Xq + R'qX. Without the assumption on ideals, the table for the multiplication need not be associative; however, if the multiplication is defined in the most obvious way to force an associative table, the new ring will still satisfy (1), (2), (3). 1. Introduction. We study nonassociative rings which satisfy the generalized right alternative law:
Proceedings of the American Mathematical Society, 1976
Let R be a nonassociative ring of characteristic different from 2 and 3 which satisfies the follo... more Let R be a nonassociative ring of characteristic different from 2 and 3 which satisfies the following identities: (i) (ab, c, d) + (a, b, [c, d]) = a(b, c, d) + (a, c, d)b, (ii) (a, a, a) = 0, (iii) (a, b " c, d) = b ° (a, c, d) + c ° (a, b, d) for all a, b, c, d G R and with x ° y = (xy + yx)/2. We prove that if R is semiprime, then R is alternative.
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Papers by Giulia Maria Cattaneo