In this paper, we consider factorizations of elements of a divisor-closed multiplicative submonoid of a ring and also factorizations of elements of a module as a product of elements coming from a divisor-closed multiplicative submonoid of the ring and another element of the module. In particular, we study uniqueness and some other properties of such factorizations and investigate the behavior of these factorizations under direct sum and product of rings and modules.
Unique factorization, bounded factorization, primitive elements, présimplifiability, divisor-closed multiplicative submonoid
NIKSERESHT, ASHKAN and AZIZI, ABDULRASOOL
"Factorization with respect to a divisor-closed multiplicative submonoid of a ring,"
Turkish Journal of Mathematics: Vol. 41:
3, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss3/2