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math.AC2025
Ideal class group of an extension of rings and Picard group
Abolfazl Tarizadeh
For any extension of commutative rings , by using invertible ideals, we first define an Abelian group $\Cl(A,B)$, that we call the ideal class group of this extension…
math.AC2025
Splitting in a complete local ring and decomposition its group of units
Abolfazl Tarizadeh
Let be a complete local ring (not necessarily Noetherian). As the first main result of this article, we prove that in the unequal characteristic case $\Char(R)\neq\Char(k…