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Monomial retracts of polynomial rings are 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 either a monic monomial or $0$. We prove that if $R$ is an integral domain, then any such retract is isomorphic to $R^{[p]}$, the polynomial ring in $p$ variables over $R$,
Chakraborty, Sagnik, Pal, Madhuparna
openaire   +2 more sources

Explicit formulas for chromatic polynomials of some series-parallel graphs

Учёные записки Казанского университета: Серия Физико-математические науки, 2018
The main goal of our paper is to present explicit formulas for chromatic polynomials of some planar series-parallel graphs (sp-graphs). The necklace-graph considered in this paper is the simplest non-trivial sp-graph.
E.Yu. Lerner, S.A. Mukhamedjanova
doaj  

On machine learning based QSPR analysis of amphetamine derivatives using regression models. [PDF]

Sci Rep
Hanif MF, Hashem AF, Hussain M, Fiidow OA.   +3 more
europepmc   +1 more source

On Double Cyclic Codes over Finite Chain Rings for DNA Computing. [PDF]

Entropy (Basel)
Ali S, Alali AS, Azeem M, Khan AA, Wong KB.   +4 more
europepmc   +1 more source

Homomorphic encryption enables privacy preserving polygenic risk scores. [PDF]

Cell Rep Methods
Knight E, Li J, Jensen M, Yolou I, Kockan C, Gerstein M.   +5 more
europepmc   +1 more source

Logarithmic-Size Post-Quantum Linkable Ring Signatures Based on Aggregation Operations. [PDF]

Entropy (Basel)
Zheng M, Huang S, Kong D, Fu X, Yao Q, Hou W.   +5 more
europepmc   +1 more source

The MacWilliams Identity for the m-Spotty Weight Enumerators over ZpRk. [PDF]

Entropy (Basel)
Wang J, Jiang A, Solé P.
europepmc   +1 more source

On the Optimal File Size of Capacity-Achieving Byzantine-Resistant Private Information Retrieval Schemes. [PDF]

Entropy (Basel)
Kruglik S, Kiah HM, Dau SH, Wang H.
europepmc   +1 more source

A novel framework for secure cryptocurrency transactions using quantum crypto guard. [PDF]

PeerJ Comput Sci
Alsayaydeh JAJ, Yusof MF, Yahaya NA, Kovtun V, Herawan SG.   +4 more
europepmc   +1 more source

A cone-beam photon-counting CT dataset for spectral image reconstruction and deep learning. [PDF]

Sci Data
Zhou E, Li W, Xu W, Wan K, Lu Y, Chen S, Zheng G, Xie T, Liu Q.   +8 more
europepmc   +1 more source