Factorization of elements in noncommutative rings, II

ABSTRACT

The mathematical object that describes the factorizations of an element a of an arbitrary ring R is the partially ordered set of all principal right ideals of R that contain aR. We present a hierarchy of situations that depend on the structure of this partially ordered set and describe the factorizations of a.

KEYWORDS:

• Factorization
• maximal left divisor
• modular lattice

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 16U30
• Secondary: 13A05
• 13F15