Establishes equivalence between τ-regularity and maximal-rank minimal projective presentations, classifies generically τ-regular components for triangular algebras, and shows hereditary algebras are precisely those with all components generically τ-regular.
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τ-regular modules are those with projective presentations of maximal rank; they form open subsets of module varieties whose closures are generically τ-regular components, with additivity of maximal rank tied to reduction to projective dimension at most one.
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Generically $\tau$-regular irreducible components of module varieties
Establishes equivalence between τ-regularity and maximal-rank minimal projective presentations, classifies generically τ-regular components for triangular algebras, and shows hereditary algebras are precisely those with all components generically τ-regular.
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On the additivity of projective presentations of maximal rank
τ-regular modules are those with projective presentations of maximal rank; they form open subsets of module varieties whose closures are generically τ-regular components, with additivity of maximal rank tied to reduction to projective dimension at most one.