Special Issue "Noncommutative Algebras, Their Applications and Generalizations"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 29 February 2020

Special Issue Editor

Guest Editor
Prof. Dr. Tomasz Brzezinski

Department of Mathematics, Swansea University, Bay Campus, Fabian Way, Swansea SA1 8EN, UK; Department of Mathematics, University of Białystok, K. Ciołkowskiego 1M, 15-245 Białystok, Poland
Website | E-Mail
Interests: noncommutative geometry; corings and comodules; Hopf algebras; category theory; algebraic structures

Special Issue Information

Dear Colleagues,

Associative algebras are one of the most fundamental and prevalent structures in modern mathematics, whether of pure or applied flavor. Their applications range from geometry through topology and analysis to physics. Traditionally commutative algebras are associated with geometry (e.g., as coordinate algebras of algebraic varieties or smooth functions on manifolds) and with classical physics (e.g., as algebras of observables in classical mechanics). Noncommutative algebras can be linked to quantum physics (e.g., as operator algebras of observables in quantum mechanics). Combining the geometric and quantum mechanical links with algebras, one can view noncommutative algebras as encoding functions on objects in noncommutative geometry.

I would like to invite contributions to this special volume which explore new developments of noncommutative algebras and related structures (such as Hopf algebras, coalgebras, or corings), in particular with their geometric meaning in mind, together with their applications to other fields. Since algebraic geometry relies heavily on categorical constructions, articles which explore connections between noncommutative algebras and category theory are most welcome. Finally, various applications of noncommutative algebras might lead to the necessity of widening the perspective and thus force one to go beyond traditional associative algebras, for example, in the direction of universal algebra considerations. Contributions leaning towards this direction are welcome, too.

Prof. Dr. Tomasz Brzezinski
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 850 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • associative algebra
  • noncommutative algebras
  • noncommutative geometry
  • algebras with additional structure (Hopf algebras, operator algebras)
  • applications of algebras in mathematics and physics

Published Papers

This special issue is now open for submission.
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