Turkish Journal of Mathematics
DOI
-
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.
Keywords
Irreducibility, associates, unique factorisation.
First Page
401
Last Page
408
Recommended Citation
AĞARGÜN, A. G. and FLETCHER, C.R. (1997) "Unique Factorisation for Commutative Rings Without Identity," Turkish Journal of Mathematics: Vol. 21: No. 4, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol21/iss4/2
