6 papers
Hilbert-Samuel functions of modules over Cohen-Macaulay rings
Srikanth Iyengar, Tony J. Puthenpurakal
For a finitely generated, non-free module over a CM local ring $(R,\fm,k)$, it is proved that for the length of $\tor 1RM{R/\fm^{n+1}}$ is given by a polynomial of deg…
A short note on the non-negativity of partial Euler characteristics
Tony J. Puthenpurakal
Let be a Noetherian local ring, a finite -module and $x_1,...,x_n\in \m$ such that $λ(M/\x M)$ is finite. Serre proved that all partial Euler characterist…
Invariance of a length associated to a reduction
Tony J. Puthenpurakal
Let be a -dimensional Cohen-Macaulay local ring with infinite residue field and let be a minimal reduction of . We show that $λ(\mathfrak{m…
The Hilbert Function of a Maximal Cohen-Macaulay Module
Tony J. Puthenpurakal
We study Hilbert functions of maximal Cohen-Macaulay(=CM) modules over CM local rings. We show that if is a hypersurface ring with dimension then the Hilbert function o…
On fiber cones of -primary ideals
A. V. Jayanthan, Tony J. Puthenpurakal, J. K. Verma
Two formulas for the multiplicity of the fiber cone $F(I)=\oplus_{n=0}^{\infty} I^n/\m I^n$ of an $\m$-primary ideal of a -dimensional Cohen-Macaulay local ring $(R,\m)$ are der…
An analogue of a theorem due to Levin and Vasconcelos
Javad Asadollahi, Tony J. Puthenpurakal
Let $(R,\m)$ be a Noetherian local ring. Consider the notion of homological dimension of a module, denoted H-dim, for H= Reg, CI, CI, G, G or CM. We prove that, if for a fi…