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Artinian local rings Whose Annihilating-ideal Graphs Are Star Graphs

Algebra Colloquium 2015年第1期22卷 73-82页

作者： Houyi Yu Tongsuo Wu Weiping Gu Department of Mathematics Southwest University Chongqing 400715 China Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China School of Mechanical Electronic & Information EngineeringChongqing College of Humanities Science &: Technology Chongqing 401524 China

In this paper, a necessary and sufficient condition is given for a commutative Artinian local ring whose annihilating-ideal graph is a star graph. Also, a complete char- acterization is established for a finite local ... 详细信息

关键词： Artinian rings local rings quotients of polynomial rings annihilating-ideals,star graphs

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Reverse mathematics and local rings

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Science China Mathematics 2024年第12期67卷 2671-2680页

作者： Huishan Wu School of Information Science Beijing Language and Culture UniversityBeijing100083China

In this paper,we study local rings from the perspective of reverse *** define local rings in a first-order way by usingΠ_2~0 properties of invertible elements,where for a ring R possibly not commutative,R is left(***)local if for any non-left(***-right)invertible elements x,y∈R,x+y is not left(***)invertible;R is local if for any non-invertible elements x,y∈R,x+y is not ***,we solve a question of Sato on characterizations of commutative local rings in his Ph D thesis(Question 6.22 in Sato(2016))and prove that the statement“a commutative ring is local if and only if it has at most one maximal ideal”is equivalent to ACA_0 over RCA_*** also obtain a nice corollary in computable mathematics,i.e.,there is a computable non-local ring with exactly two maximal ideals such that each of them Turing computes the Halting set ***,we study the equivalence among left local rings,right local rings,and local rings,showing that these three kinds of first-order local rings are equivalent over the weak basis theory RCA_***,we extend the results of reverse mathematics on commutative local rings to noncommutative rings.

关键词： reverse mathematics noncommutative rings local rings maximal ideals

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A Note on Skew Cyclic Codes over a Class of rings

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Algebra Colloquium 2020年第4期27卷 703-712页

作者： Hai Q.Dinh Bac T.Nguyen Songsak Sriboonchitta Division of Computational Mathematics and Engineering Institute for Computational Science Ton Due Thang University Ho Chi Minh CityVietnam Faculty of Mathematics and Statistics Ton Due Thang University Ho Chi Minh CityVietnam Department of Basic Sciences University of Economics and Business Administration Thai Nguyen UniversityThai Nguyen ProvinceVietnam Centre of Excellence in Econometrics Faculty of Economics Chiang Mai UniversityChiang Mai 52000Thailand

We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite *** prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over ***,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.

关键词： skew constacyclic codes dual codes repeated-root codes quasi-cyclic codes local rings

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Constacyclic Codes of Length Ps over Finite rings FPm+uFPm+vFPm+uvFPm

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Wuhan University Journal of Natural Sciences 2020年第4期25卷 311-322页

作者： HU Peng LIU Xiusheng School of Mathematics and Physics Hubei Polytechnic UniversityHuangshi 435003HubeiChina

Let R-Fpm+uFpm+vFpm+uvFpm,where u2=v2=0,uv=*** R is a local ring,but it is not a chain ring.R contains precisely(pm-1)p3 m units,namely,α+uβ+vγ+uvδ,where α,β,γ,δ∈Fpm,α≠*** this paper,we investigate all constacyclic codes of length ps over ***,we classify allα-constacyclic and(α+uvβ)-constacyclic codes of length ps over R,respectively,and obtain their structure in each of thoseα-constacyclic and(α+uvβ)-constacyclic ***,we address the(α+uβ)-constacyclic codes of length ps over R,and get their classification and ***,using similar discussion of(α+uβ)-constacyclic codes,we obtain the classification and the structure of α+vβ,α+uβ+uvγ,α+vβ+uvγ,α+uβ+vγ,α+uβ+vβ+uvδ-constacyclic codes of length ps over R.

关键词： constacyclic codes local rings ideals

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