Factorization with respect to a divisor-closed multiplicative submonoid of a ring

Authors : Ashkan NIKSERESHT, Abdulrasool AZIZI

Pages : 483-499

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :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.
Keywords : Unique factorization, bounded factorization, primitive elements, présimplifiability, divisor closed multiplicative submonoid