Unique factorization in Cayley arithmetics and cryptology
نویسندگان
چکیده
منابع مشابه
Foundations and Unique Factorization
This is a difficult question to answer: number theory is an area, or collection of areas, of pure mathematics that have been studied for well over two thousand years. As such, it means different things to different number theorists (of which I am one). Nevertheless the question is not nearly as subjective as “What is truth?” or “What is beauty?”: all of the things that various people call numbe...
متن کاملUnique Factorization Monoids and Domains
It is the purpose of this paper to construct unique factorization (uf) monoids and domains. The principal results are: (1) The free product of a well-ordered set of monoids is a uf-monoid iff every monoid in the set is a uf-monoid. (2) If M is an ordered monoid and F is a field, the ring ^[[iW"]] of all formal power series with well-ordered support is a uf-domain iff M is naturally ordered (i.e...
متن کاملUnique factorization in perturbative QFT
Over recent years, the Lie and Hopf algebra structures of Feynman graphs have been firmly established in collaboration with Alain Connes and David Broadhurst [1–11]. Hopefully, they find their way now into the algorithmic toolkit of the practitioner of QFT. They directly address the computational practice of momentum space Feynman integrals, but can be equivalently formulated in coordinate spac...
متن کاملUnique Factorization in Integral Domains
Throughout R is an integral domain unless otherwise specified. Let A and B be sets. We use the notation A ⊆ B to indicate that A is a subset of B and we use the notation A ⊂ B to mean that A is a proper subset of B. The group of elements in R which have a multiplicative inverse (the group of units of R) is denoted R×. Since R has no zero divisors cancellation holds. If a, b, c ∈ R and a 6= 0 th...
متن کاملOn Unique Factorization Semilattices
The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1991
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500008326