Classification of Rings Associated with the Genus of Clean Graphs

作     者：V.Ramanathan C.Selvaraj Aaqib Altaf S.Pirzada 

作者机构：Department of MathematicsPeriyar UniversitySalem 636011Tamil NaduIndi Department of MathematicsUniversity of KashmirHazratbalSrinagarKashmirIndia 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2024年第31卷第3期

页      面：451-466页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by Dr.D.S.Kothari Postdoctoral Fellowship Scheme(No.F.4-2/2006(BSR)/MA/17-18/0045)of University Grants Commission,India,awarded to the first author the second author was supported by UGC SAP DRS-1(No.F.510/7/DRS-1/2016(SAP-I),University Grants Commission,Government of India The research of S.Pirzada was supported by SERB-DST research project number CRG/2020/000109 

主　　题：clean graph commutative ring planar graph genus crosscap 

摘      要：Let R be a ring(not necessarily commutative)with identity 1 and let CL(R)be its clean *** this paper,we investigate the genus number of the compact Riemann surface in which CL(R)can be embedded and explicitly determine all commutative rings R(up to isomorphism)such that CL(R)has genus at most *** is shown that for any Artinian ring R,CL(R)is a projective graph if and only if R is isomorphic to ***,we determine all isomorphism classes of commutative rings whose clean graphs have crosscap two.