On euclidean norms and factorization in ternary semi-domains

In this paper, general properties of right divisors and greatest common right divisors in a ternary semiring are considered. The notion of left Euclidean norm on a ternary semiring is introduced to characterize the existence of the greatest common right divisor of a non-empty finite subset in a principal left ideal subtractive ternary semiring. The relationships of left Euclidean ternary semirings with principal left ideal subtractive ternary semirings, greatest common right divisor ternary semidomains, factorization ternary semi-domains and discrete valuation ternary semirings are also established.