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 Universite 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.
R. R. de Araujo, A. L. M. Pereira, and C. Polcino Milies, A note on
checkable codes over Frobenius and quasi-Frobenius rings
N. Aydin, T. Guidotti, and P. Liu, Good classical and quantum codes from
multi-twisted codes
N. Bennenni and A. Leroy, Evaluation of iterated ore polynomials and skew
Reed-Muller codes
G. Blachar, L. H Rowen, and U. Vishne, Identities of the algebra
$\mathbb{O}\otimes\mathbb{O}$
S. Breaz and Y. Zhou, When is every non central-unit a sum of two
nilpotents?
A. Chapman and K. McKinnie, Asymptotic Brauer $p$-dimension
L. W. Christensen, S. Estrada, and P. Thompson, Five theorems on Gorenstein
global dimensions
S. T. Dougherty and S. Sahinkaya, Quasi-self-dual codes over a non-unital
ring of order 4
S. T. Dougherty, S. Sahinkaya, and D. Ustun, Codes from the skew ring
$M_2(\mathbb{F}_2\rtimes_\varphi G$
F. D'Este, The underlying vector spaces of certain endomorhism rings
A. Facchini, Algebraic structures from the point of view of complete
multiplicative lattices
C. Fernandez-Cordoba and S. Szabo, $\mathbb{Z}_2\mathbb{Z}_4$-additive codes
as codes over rings
G. Lee, C. S. Roman, N. K. Tung, and X. Zhang, On Utumi rings and continuous
regular Baer rings
S. K. Jain and A. Leroy, Matrices representable as product of conjugates of a
singular matrix
F. Kaynarca, G. D'Este, and D. Keskin Tutuncu, Almost projective modules over
non-hereditary algebras
M. Salahuddin Khan, A. Abbasi, S. Ali, and M. Ayedh, On prime ideals with
generalized derivations in rings with involution
J. Krempa, On nil algebras and a problem of Passeman concerning nilpotent
free algebras
X. Mary, Rings with transitive chaining of idempotents
J. K. Park and S. T. Rizvi, On continuous hulls of rings and modules
A. Leroy, Universite d'Artois, Lens, France.
S. K. Jain, Ohio University, Athens, OH.
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