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This is a contribution to the theory of atoms in abelian categories recently developed in a series of papers by Kanda. We present a method that enables one to explicitly compute the atom spectrum of the module category over a wide range of non-commutative rings. We illustrate our method and results by several examples.We prove Theorem A in Section 4, where we also give the definitions of admisible relations (4.3), right-rooted quivers (4.1), and of the ideals p(i) (4.11). In the terminology 2010 Mathematics Subject Classification. 16G20; 18E10.

This is a contribution to the theory of atoms in abelian categories recently developed in a series of papers by Kanda. We present a method that enables one to explicitly compute the atom spectrum of the module category over a wide range of non‐commutative rings. We illustrate our method and results by several examples.