Managing editor: M Hazewinkel.

Editorial board: M. Artin, M. Nagata, C. Procesi, O. Tausky-Todd†, R.G. Swan, P.M. Cohn, A. Dress, J. Tits, N.J.A. Sloane, C. Faith, S.I. A’dyan, Y. Ihara, L. Small, E. Manes, I.G. Macdonald, M. Marcus, L.A. Bokut', Eliezer (Louis Halle) Rowen, John S. Wilson, Vlastimil Dlab. Note that three editors have been added starting with Volume 5.

2001: Volume 2 (published)

2003: Volume 3 (published)

2005: Volume 4 (published)

2007: Volume 5 (last quarter)

G.P. Egorychev, Van der Waerden conjecture and applications (1; 22 pp.)

V.L. Girko, Random matrices (1; 52 pp.)

A.N. Malyshev, Matrix equations. Factorization of matrices (1; 38 pp.)

L. Rodman, Matrix functions (1; 38 pp.)

Correction to the chapter by L. Rodman, Matrix functions (3; 1 p.)

J.A. Hermida-Alonso, Linear algebra over commutative rings (3; 49 pp.)

Linear inequalities (also involving matrices)

Orderings (partial and total) on vectors and matrices

Positive matrices

Structured matrices such as Toeplitz and Hankel

Integral matrices. Matrices over other rings and fields.

Quasideterminants, and determinants over noncommutative fields.

Nonnegative matrices, positive definite matrices, and doubly nonnegative matrices.

Linear algebra over skew fields

J.P.S. Kung, Matroids (1; 28 pp.)

Clifford algebras, related algebras, and applications

Other algebras arising from vector spaces (working title only)

(There is also a chapter on ordered fields in Section 4)

J.K. Deveney, J.N. Mordeson, Higher derivation Galois theory of inseparable field extensions (1; 34 pp.)

I. Fesenko, Complete discrete valuation fields. Abelian local class field theories (1; 48 pp.)

M. Jarden, Infinite Galois theory (1; 52 pp.)

R. Lidl, H. Niederreiter, Finite fields and their applications (1; 44 pp.) W. Narkiewicz, Global class field theory (1; 30 pp.)

H. van Tilborg, Finite fields and error correcting codes (1; 28 pp.)

Skew fields and division rings. Brauer group

Topological and valued fields. Valuation theory

Zeta and L-functions of fields and related topics

Structure of Galois modules

Constructive Galois theory (realizations of groups as Galois groups)

Dessins d’enfants

Hopf Galois theory

T. Albu, From field theoretic to abstract co-Galois theory (5; 81 pp.)

(to be arranged in several chapters by Y. Ihara)

U. Hebisch, H.J. Weinert, Semi-rings and semi-fields (1; 38 pp.)

G. Pilz, Near rings and near fields (1; 36 pp.)

S. MacLane, I. Moerdijk, Topos theory (1; 28 pp.)

R. Street, Categorical structures (1; 50 pp.)

B.I. Plotkin, Algebra, categories and databases (2; 71 pp.)

P.S. Scott, Some aspects of categories in computer science (2; 71 pp.)

E. Manes, Monads of sets (3; 48 pp.)

M. Markl, Operads and PROPs (5; 54 pp.)

J.F. Carlson, The cohomology of groups (1; 30 pp.)

A. Generalov, Relative homological algebra. Cohomology of categories, posets, and coalgebras (1; 28 pp.)

J.F. Jardine, Homotopy and homotopical algebra (1; 32 pp.)

B. Keller, Derived categories and their uses (1; 32 pp.)

A.Ya. Helemskii, Homology for the algebras of analysis (2; 143 pp.))

Galois cohomology

Cohomology of commutative and associative algebras

Cohomology of Lie algebras

Cohomology of group schemes

V. Lyubashenko, O. Manzyuk, A$$-algebras, A$$-categories, and A$$-functors (5; 46 pp.)

B.V. Novikov, 0-Cohomology of semigroups (5; 21 pp.)

A. Kuku, Classical algebraic K-theory: the functors K0, K1, K2 (3; 55 pp.)

A. Kuku, Algebraic K-theory: the higher K-functors (4; 122 pp.)

Grothendieck groups

K2 and symbols

KK-theory and EXT

Hilbert C* -modules

Index theory for elliptic operators over C* algebras

Simplicial algebraic K-theory

Chern character in algebraic K-theory

Noncommutative differential geometry

K-theory of noncommutative rings

Algebraic L-theory

Cyclic cohomology

Asymptotic morphisms and E-theory

Hirzebruch formulae

(See also P.C. Eklof, Whitehead modules, in Section 3B)

M. Prest, Model theory for algebra (3; 31 pp.)

M. Prest, Model theory and modules (3; 34 pp.)

Logical properties of fields and applications

Recursive algebras

Logical properties of Boolean algebras

F.O. Wagner, Stable groups (2; 36 pp.)

The Ax–Ershov–Kochen theorem and its relatives and applications

Rings up to homotopy

Simplicial algebras

(See also C. Faith, Coherent rings and annihilator conditions in matrix and polynomial rings, in Section 3B)

(See also Freeness theorems for group rings and Lie algebras in Section 5A)

J.P. Lafon, Ideals and modules (1; 24 pp.)

General theory. Radicals, prime ideals, etc. Local rings (general). Finiteness and chain conditions

Extensions. Galois theory of rings

Modules with quadratic form

Homological algebra and commutative rings. Ext, Tor, etc. Special properties (p.i.d., factorial, Gorenstein,...