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Algebra and Coding Theory
 
Edited by: A. Leroy Université d’Artois, Lens, France
S. K. Jain Ohio University, Athens, OH
Softcover ISBN:  978-1-4704-6859-0
Product Code:  CONM/785
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-1-4704-7298-6
Product Code:  CONM/785.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6859-0
eBook: ISBN:  978-1-4704-7298-6
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
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Algebra and Coding Theory
Edited by: A. Leroy Université d’Artois, Lens, France
S. K. Jain Ohio University, Athens, OH
Softcover ISBN:  978-1-4704-6859-0
Product Code:  CONM/785
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-1-4704-7298-6
Product Code:  CONM/785.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6859-0
eBook ISBN:  978-1-4704-7298-6
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 Details
     
     
    Contemporary Mathematics
    Volume: 7852023; 253 pp
    MSC: 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.

    Readership

    Graduate 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 quasi-Frobenius rings
    • Nuh Aydin, Thomas Guidotti and Peihan Liu — Good classical and quantum codes from multi-twisted codes
    • Nabil Bennenni and André Leroy — Evaluation of iterated Ore polynomials and skew Reed-Muller 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 Central-Unit 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 — Quasi-Self-Dual Codes over a Non-Unital 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 Fernández-Córdoba 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 Non-Hereditary 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
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 7852023; 253 pp
MSC: 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.

Readership

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 quasi-Frobenius rings
  • Nuh Aydin, Thomas Guidotti and Peihan Liu — Good classical and quantum codes from multi-twisted codes
  • Nabil Bennenni and André Leroy — Evaluation of iterated Ore polynomials and skew Reed-Muller 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 Central-Unit 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 — Quasi-Self-Dual Codes over a Non-Unital 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 Fernández-Córdoba 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 Non-Hereditary 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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