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Softcover ISBN:  9781470468590 
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Softcover ISBN:  9781470468590 
Product Code:  CONM/785 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9781470472986 
Product Code:  CONM/785.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470468590 
eBook ISBN:  9781470472986 
Product Code:  CONM/785.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 785; 2023; 253 ppMSC: Primary 16; 11; 94
This volume contains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, in honor of Tariq Rizvi, held from July 5–7, 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held on July 8, 2021, both of which were hosted by the Université d'Artois, Lens, France.
The articles cover topics in commutative and noncommutative algebra and applications to coding theory. In some papers, applications of Frobenius rings, the skew group rings, and iterated Ore extensions to coding theory are discussed. Other papers discuss classical topics, such as Utumi rings, Baer rings, nil and nilpotent algebras, and Brauer groups. Still other articles are devoted to various aspects of the elementwise study for rings and modules. Lastly, this volume includes papers dealing with questions in homological algebra and lattice theory. The articles in this volume show the vivacity of the research of noncommutative rings and its influence on other subjects.
ReadershipGraduate students and research mathematicians interested in noncommutative algebras and codes.

Table of Contents

Articles

R. R. de Araujo, A. L. M. Pereira and C. Polcino Milies — A note on checkable codes over Frobenius and quasiFrobenius rings

Nuh Aydin, Thomas Guidotti and Peihan Liu — Good classical and quantum codes from multitwisted codes

Nabil Bennenni and André Leroy — Evaluation of iterated Ore polynomials and skew ReedMuller codes

Guy Blachar, Louis H. Rowen and Uzi Vishne — Identities of the algebra $\mathbb {O} \otimes \mathbb {O}$

Simion Breaz and Yiqiang Zhou — When Is Every Non CentralUnit A Sum of Two Nilpotents?

Adam Chapman and Kelly McKinnie — Asymptotic Brauer $p$dimension

Lars Winther Christensen, Sergio Estrada and Peder Thompson — Five theorems on Gorenstein global dimensions

Steven T. Dougherty and Serap Şahinkaya — QuasiSelfDual Codes over a NonUnital Ring of Order $4$

S. T. Dougherty, Serap Şahinkaya and Deniz Ustun — Codes from the Skew Ring $M_2(\mathbb {F}_2)\rtimes _{\varphi }G$

Gabriella D’Este — The underlying vector spaces of certain endomorphism rings

Alberto Facchini — Algebraic structures from the point of view of complete multiplicative lattices

Cristina FernándezCórdoba and Steve Szabo — $\mathbb {Z}_2\mathbb {Z}_4$additive codes as codes over rings

Gangyong Lee, Cosmin S. Roman, Nguyen Khanh Tung and Xiaoxiang Zhang — On Utumi rings and continuous regular Baer rings

S. K. Jain and André Leroy — Matrices representable as product of conjugates of a singular matrix

Fatma Kaynarca, Gabriella D’Este and Derya Keskin Tütüncü — Almost Projective Modules Over NonHereditary Algebras

Mohammad Salahuddin Khan, Adnan Abbasi, Shakir Ali and Mohammed Ayedh — On prime ideals with generalized derivations in rings with involution

Jan Krempa — On nil algebras and a problem of Passman concerning nilpotent free algebras

Xavier Mary — Rings with transitive chaining of idempotents

Jae Keol Park and S. Tariq Rizvi — On Continuous Hulls of Rings and Modules


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This volume contains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, in honor of Tariq Rizvi, held from July 5–7, 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held on July 8, 2021, both of which were hosted by the Université d'Artois, Lens, France.
The articles cover topics in commutative and noncommutative algebra and applications to coding theory. In some papers, applications of Frobenius rings, the skew group rings, and iterated Ore extensions to coding theory are discussed. Other papers discuss classical topics, such as Utumi rings, Baer rings, nil and nilpotent algebras, and Brauer groups. Still other articles are devoted to various aspects of the elementwise study for rings and modules. Lastly, this volume includes papers dealing with questions in homological algebra and lattice theory. The articles in this volume show the vivacity of the research of noncommutative rings and its influence on other subjects.
Graduate students and research mathematicians interested in noncommutative algebras and codes.

Articles

R. R. de Araujo, A. L. M. Pereira and C. Polcino Milies — A note on checkable codes over Frobenius and quasiFrobenius rings

Nuh Aydin, Thomas Guidotti and Peihan Liu — Good classical and quantum codes from multitwisted codes

Nabil Bennenni and André Leroy — Evaluation of iterated Ore polynomials and skew ReedMuller codes

Guy Blachar, Louis H. Rowen and Uzi Vishne — Identities of the algebra $\mathbb {O} \otimes \mathbb {O}$

Simion Breaz and Yiqiang Zhou — When Is Every Non CentralUnit A Sum of Two Nilpotents?

Adam Chapman and Kelly McKinnie — Asymptotic Brauer $p$dimension

Lars Winther Christensen, Sergio Estrada and Peder Thompson — Five theorems on Gorenstein global dimensions

Steven T. Dougherty and Serap Şahinkaya — QuasiSelfDual Codes over a NonUnital Ring of Order $4$

S. T. Dougherty, Serap Şahinkaya and Deniz Ustun — Codes from the Skew Ring $M_2(\mathbb {F}_2)\rtimes _{\varphi }G$

Gabriella D’Este — The underlying vector spaces of certain endomorphism rings

Alberto Facchini — Algebraic structures from the point of view of complete multiplicative lattices

Cristina FernándezCórdoba and Steve Szabo — $\mathbb {Z}_2\mathbb {Z}_4$additive codes as codes over rings

Gangyong Lee, Cosmin S. Roman, Nguyen Khanh Tung and Xiaoxiang Zhang — On Utumi rings and continuous regular Baer rings

S. K. Jain and André Leroy — Matrices representable as product of conjugates of a singular matrix

Fatma Kaynarca, Gabriella D’Este and Derya Keskin Tütüncü — Almost Projective Modules Over NonHereditary Algebras

Mohammad Salahuddin Khan, Adnan Abbasi, Shakir Ali and Mohammed Ayedh — On prime ideals with generalized derivations in rings with involution

Jan Krempa — On nil algebras and a problem of Passman concerning nilpotent free algebras

Xavier Mary — Rings with transitive chaining of idempotents

Jae Keol Park and S. Tariq Rizvi — On Continuous Hulls of Rings and Modules