Attached primes over noncommutative rings

Attached primes and secondary representations were introduced in 1973 by Macdonald [I.G. Macdonald, Secondary representation of modules over a commutative ring, Sympos. Math. 11 (1973) 23-43] to develop a dual theory to the associated primes and primary decomposition in commutative algebra. This article generalizes Macdonald’s theory to the noncommutative setting.