Gluing of idempotents, radical embeddings and two classes of stable equivalences

Stable equivalences are studied between any finite dimensional algebra A with a simple projective module and a simple injective module and an algebra B obtained from A by ‘gluing’ the corresponding idempotents of A; this extends results by Martinez-Villa. Stable equivalences modulo projectives are compared to stable equivalences modulo semisimples, and in either situation a characterization is given for a radical embedding to induce such a stable equivalence.