What question did this study set out to answer?

To explore the connections between fundamental invariants of Artinian local algebras, particularly in Gorenstein cases.

On certain invariants of commutative Artinian algebras

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To explore the connections between fundamental invariants of Artinian local algebras, particularly in Gorenstein cases.
Analyzed the modules of derivations and Kähler differentials for local Artinian Gorenstein algebras.
Utilized duality theories in the cotangent complex of analytic algebras.
Examined the structures of annihilators and socles in relation to the invariants.
Demonstrated that the length of modules of derivations and Kähler differentials is at most one less than that of the algebra.
Established that the Tyurina number is always greater than or equal to the Milnor number in smoothable zero-dimensional Gorenstein singularities.

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Shows the relationship between algebraic invariants in Artinian algebras, indicating important inequalities.

A. Aleksandrov (2026) studied this question.

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