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The development of associative algebra during the last century has resulted in the emergence of numerous theories or specialties that have offered solutions to many of the needs of the society in which we live, increasingly developed from a technological point of view.
These needs fall into two broad groups: purely technological needs and theoretical needs associated with developments in both applied algebra and other branches of mathematics. After all, it is not unreasonable to think that algebra is something like the "mathematics of mathematics".
There are many branches of algebra whose contributions solve problems posed by the scientific challenges arising from the advancement of technology. Two of them also stand out for their popularity in society: cryptography and coding theory.
In addition, from a theoretical point of view, the momentum that some disciplines have experienced in the last 20 years is remarkable. Thus, homological algebra has been given a big push with the emergence of the different classes of Gorenstein modules and, in recent years, in particular, the relative Gorenstein modules. Moreover, the emergence of C*-algebras has had a huge impact on many branches of mathematics and physics, and, of course, one cannot forget the very active branches of modules over non-commutative rings and derivations in algebras, with immense applications at all times.
We are therefore pleased to present this Special Issue of Mathematics as a tool to share recent and compelling advancements in the branches of homological algebra, module theory, C*-algebras, coding theory, and derivations in algebras.
