Turkish Journal of Mathematics
Abstract
This paper concerns the unique factorisation property in commutative rings not necessarily with identity. We give a new definition of irreducibility and associates in a commutative ring with 1 (crwl), and define a UFR R in terms of a monomorphism from R into a crwl. This becomes equivalent to the definition in [3] when R has an identity. We generalize results on direct sums and direct summands. By our definition we have new members of the family of UFR's.
DOI
-
Keywords
Irreducibility, associates, unique factorisation.
First Page
401
Last Page
408
Recommended Citation
AĞARGÜN, A. G, & FLETCHER, C (1997). Unique Factorisation for Commutative Rings Without Identity. Turkish Journal of Mathematics 21 (4): 401-408. https://doi.org/-
