AWMA virtual seminar n°22

The speaker Dr. Sarah Nakato is a mathematics lecturer at Kabale University, Uganda.

She completed her Ph.D. studies at Graz University of Technology, Austria, in 2020 and continued working for two years at the same university as a postdoctoral researcher. Her research interests lie in commutative algebra, factorization theory, integer-valued polynomials, and cryptography.

She is a co-founder and current convenor of the African Women in Algebra, an association that brings together African women working in algebra and its applications. She was also the group leader/lecturer for the Algebra group at the Women in Sage -Uganda workshop.

She is enthusiastic about giving back to the mathematics community; for instance, she is a mentor under Mfano Africa and runs Facebook groups for mathematics job announcements and stipends: Mathematics scholarships and Mathematics Scholarships II.



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Date Thursday,  October 26, 2023
Time 14:00-15:00 (UTC)
Speaker Dr. Sarah NAKATO
Affiliation Kabale University, Uganda
Domain Algebra
Title  Sets lengths of integer valued polynomials

The set of lengths of an element r is the set of all natural numbers n such that r has a factorization of length n. Sets of lengths are the most investigated invariants in factorization theory. They fully describe the factorization behaviour of the structure, and we can deduce certain invariants from them. Such investigations give information about the arithmetical and algebraic properties of the algebraic structures under consideration.

In this talk, we focus on the ring of integer-valued polynomials,

Int(D) = {f in K[x] : for all a in D, f(a) is in D }, where D is a domain with quotient field K.

We present two main results for special domains D. First, for any finite multiset N of natural numbers greater than 1, there exists a polynomial f in Int(D) that has exactly |N| essentially different factorizations of the prescribed lengths.

In particular, this implies that every finite non-empty set N of natural numbers greater than 1 occurs as a set of lengths of a polynomial f in Int(D). Second, we show that the multiplicative monoid Int(D)\{0} of Int(D) is not a transfer Krull monoid.

  • Find attached the slides of the talk.
Thursday, October 26, 2023