مؤسسة الشرق الأوسط للنشر العلمي
عادةً ما يتم الرد في غضون خمس دقائق
This research establishes a new paradigm in non-commutative homological algebra through the definitive resolution of several long-standing conjectures and the introduction of powerful new theoretical frameworks, we present three principal theorems. First, we provide a complete characterization of the Gorenstein property for coherent rings, proving it is equivalent to the ring's derived category being a fractional Calabi-Yau category; this result leads to a new homological invariant, the Gorenstein index, which measures the "quantum twist" of a ring's duality. Second, we provide an unconditional proof of the Strong No Loop Conjecture for Artinian algebras, a foundational problem in representation theory, third, we establish a precise formula governing the asymmetry of left and right global dimensions for Noetherian rings, linking this difference to a K-theoretic obstruction we term the homological torsion, Iwasawa algebras, and a complete, theory-driven computation of the homological dimensions of the skew first Weyl algebra.