Extensions of Abelian Categories and the Strong No-Loops Conjecture Original Research Article

Given a ring A, we form its truncated extensions A[formula]lM. We study the extension groups ExtnA[formula]lM(X,Y) in relation to ExtnA(X,Y), n set membership, variant image union or logical sum {0}. If AM is flat, then using the theory of spectral sequences, we obtain a precise formula for ExtnA[formula]lM(X,Y) for simple (A[formula]lM)-modules. We also obtain bounds for gl.dim A[formula]lM. In the case A is a semisimple ring, we prove the truth of the Strong No-Loops Conjecture for A[formula]lM.