Displaying 221 – 240 of 384

Showing per page

On the Delta set of a singular arithmetical congruence monoid

Paul Baginski, Scott T. Chapman, George J. Schaeffer (2008)

Journal de Théorie des Nombres de Bordeaux

If a and b are positive integers with a b and a 2 a mod b , then the set M a , b = { x : x a mod b or x = 1 } is a multiplicative monoid known as an arithmetical congruence monoid (or ACM). For any monoid M with units M × and any x M M × we say that t is a factorization length of x if and only if there exist irreducible elements y 1 , ... , y t of M and x = y 1 y t . Let ( x ) = { t 1 , ... , t j } be the set of all such lengths (where t i < t i + 1 whenever i < j ). The Delta-set of the element x is defined as the set of gaps in ( x ) : Δ ( x ) = { t i + 1 - t i : 1 i < k } and the Delta-set of the monoid M is given by x M M × Δ ( x ) . We consider the Δ ( M ) when M = M a , b is an ACM with...

Currently displaying 221 – 240 of 384