Abstract
Let be an (S, R)-bimodule of the rings R and S. We determine the associated primes of a formal triangular matrix ring
Indeed, we show that
We then obtain necessary and sufficient conditions for the tertiary decomposition theory to exist on a module over an arbitrary ring. Consequently, we classify all the tertiary right ideals of the formal triangular matrix rings.
Disclosure statement
No potential conflict of interest was reported by the authors.