Puthenpurakal, Tony J.Tony J.PuthenpurakalRoy, SudeshnaSudeshnaRoy2025-08-312025-08-312025-11-0110.1016/j.jalgebra.2025.05.0112-s2.0-105006790600https://d8.irins.org/handle/IITG2025/27998Let A be a Dedekind domain of characteristic zero such that its localization at every maximal ideal has mixed characteristic with finite residue field. Let R=A[X<inf>1</inf>,…,X<inf>n</inf>] be a polynomial ring and I=(a<inf>1</inf>U<inf>1</inf>,…,a<inf>c</inf>U<inf>c</inf>)⊆R an ideal, where a<inf>j</inf>∈A (not necessarily units) and U<inf>j</inf>'s are monomials in X<inf>1</inf>,…,X<inf>n</inf>. We call such an ideal I as a C-monomial ideal. Consider the standard multigrading on R. We produce a structure theorem for the multigraded components of the local cohomology modules H<inf>I</inf>ⁱ(R) for i≥0. We further analyze the torsion part and the torsion-free part of these components. We show that if A is a PID then each component can be written as a direct sum of its torsion part and torsion-free part. As a consequence, we obtain that their Bass numbers are finite.falseBass numbers | Local cohomology | Monomial ideals | Multigraded local cohomologyArticle1090266X1-211 November 20250arJournal0