arXiv subjects

Madhuparna Pal

Publications and source records attributed to Madhuparna Pal.

2 recordsLinked to original sources

arXiv2026

Monomial and binomial retracts of polynomial rings

Let $R$ be a ring and $B := R[X_1, \dots, X_n]$ the polynomial ring in $n$ variables over $R$. In this article, we consider retractions $φ: B \longrightarrow B$ such that $φ(X_i)$ is $0$, or a monomial or the sum of two monomials. We prove that, under certain conditions on the base ring $R$, the resulting retracts are also polynomial rings over $R$. We characterize different monomial retractions of $B$, i.e., where $φ(X_i)$ is $0$ or a monomial for all $i$, giving the same retract. We also generalize the structure of monomial retracts by allowing a few variables to map to arbitrary polynomials, but only under some additional restrictions on the base ring $R$.

math.AC↗

arXiv2026

Derivations of plane algebroid curves

In this paper, we study the derivations of an irreducible plane algebroid curve $R:=\frac{k[[X,Y]]}{(f)}$, which is not regular. Since the normalization of $R$ is isomorphic to $k[[t]]$, every $k$-derivation of $R$ is induced from a $k$-derivation of $k[[t]]$, which are of the form $a(t)\frac{d}{dt}$ for some $a(t)\in k[[t]]$. We establish a lower bound on the $t$-order of a nonzero power series $a(t)$ for $a(t)\frac{d}{dt}$ to induce a derivation of $R$ in terms of the multiplicity of $R$. We also prove a related result for the value semi-group of such curves.

math.AC↗