Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results.
This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic K-theories,...

While in classical (abelian) homological algebra additive functors from abelian (or additive) categories to abelian categories are investigated, non- abelian homological algebra deals with non-additive functors and their homological properties, in particular with functors having values in non-abelian categories. Such functors haveimportant applications in algebra, algebraic topology, functional analysis, algebraic geometry and other principal areas of mathematics. To study homological properties of non-additive functors it is necessary to define and investigate their derived functors and...

Tbilisi Mathematical Journal (TMJ) is a fully refereed international journal, publishing original research papers in all areas of mathematics. Papers should satisfy the high standards and only works of high quality will be recommended for publication. The Management Committee may occasionally decide to invite the submission of survey and expository papers of the highest quality. Unsolicited submissions of survey and expository papers will not be considered for publication. Volume 1 (2008) contains eight research papers by outstanding mathematicians in areas ranging from functional analysis to...

Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results.
This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic K-theories,...

While in classical (abelian) homological algebra additive functors from abelian (or additive) categories to abelian categories are investigated , non- abelian homological algebra deals with non-additive functors and their homological properties , in particular with functors having values in non-abelian categories. Such functors haveimportant applications in algebra, algebraic topology, functional analysis, algebraic geometry and other principal areas of mathematics. To study homological properties of non-additive functors it is necessary to define and investigate their derived functors and...

Tbilisi Mathematical Journal (TMJ) is a fully refereed international journal, publishing original research papers in all areas of mathematics. Papers should satisfy the high standards and only works of high quality will be recommended for publication. The Management Committee may occasionally decide to invite the submission of survey and expository papers of the highest quality. Unsolicited submissions of survey and expository papers will not be considered for publication. Volume 3 (2010) contains two research papers by outstanding mathematicians.