Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.

• 1 Radicals, local and semisimple modules.- 1.1 Maximal submodules and the Jacobson radical.- 1.2 Local and uniserial modules.- 1.3 Semisimple and Artinian modules.- 1.4 The prime radical.- 2 Projective and injective modules.- 2.1 Free and projective modules.- 2.2 Injective modules.- 2.3 Injective hull.- 3 Bezout and regular modules.- 3.1 Regular modules.- 3.2 Unit-regular rings.- 3.3 Semilocal rings and distributivity.- 3.4 Strongly regular rings.- 3.5 Bezout rings.- 4 Continuous and finite-dimensional modules.- 4.1 Closed submodules.- 4.2 Continuous modules.- 4.3 Finile-dimensional modules.- 4.4 Nonsingular ?-injective modules.- 5 Rings of quotients.- 5.1 Ore sets.- 5.2 Denominator sets and localizable rings.- 5.3 Maximal rings of quotients.- 6 Flat modules and semiperfect rings.- 6.1 Characterizations of flat modules.- 6.2 Submodules of flat modules.- 6.3 Semiperfect and perfect rings.- 7 Semihereditary and invariant rings.- 7.1 Coherent and reduced rings.- 7.2 Invariant rings.- 7.3 Rings with integrally closed factor rings.- 8 Endomorphism rings.- 8.1 Modules over endomorphism rings and quasi injective modules.- 8.2 Nilpotent endomorphisms.- 8.3 Strongly indecomposable modules.- 9 Distributive rings with maximum conditions.- 9.1 Arithmetics of ideals.- 9.2 Noel.herian rings.- 9.3 Classical rings of quotients of distributive rings.- 9.4 Rings algebraic over their centre.- 10 Self-injective and skew-injective rings.- 10.1 Quasi-frobenius rings and direct sums of injective modules.- 10.2 Cyclic ?-injective modules.- 10.3 Integrally closed Noetherian rings.- 10.4 Cyclic skew-injective modules.- 10.5 Countably injective rings.- 11 Semidistributive and serial rings.- 11.1 Semidistributive modules.- 11.2 Semidistributive rings.- 11.3 Serial modules and rings.- 12 Monoidrings and related topics.- 12.1 Series and polynomial rings.- 12.2 Quaternion algebras.- 12.3 Subgroups, submonoids, and annihilators.- 12.4 Regular group rings.- 12.5 Cancellative monoids.- 12.6 Semilattices and regular monoids.

Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.

• 1 Radicals, local and semisimple modules.- 1.1 Maximal submodules and the Jacobson radical.- 1.2 Local and uniserial modules.- 1.3 Semisimple and Artinian modules.- 1.4 The prime radical.- 2 Projective and injective modules.- 2.1 Free and projective modules.- 2.2 Injective modules.- 2.3 Injective hull.- 3 Bezout and regular modules.- 3.1 Regular modules.- 3.2 Unit-regular rings.- 3.3 Semilocal rings and distributivity.- 3.4 Strongly regular rings.- 3.5 Bezout rings.- 4 Continuous and finite-dimensional modules.- 4.1 Closed submodules.- 4.2 Continuous modules.- 4.3 Finile-dimensional modules.- 4.4 Nonsingular ?-injective modules.- 5 Rings of quotients.- 5.1 Ore sets.- 5.2 Denominator sets and localizable rings.- 5.3 Maximal rings of quotients.- 6 Flat modules and semiperfect rings.- 6.1 Characterizations of flat modules.- 6.2 Submodules of flat modules.- 6.3 Semiperfect and perfect rings.- 7 Semihereditary and invariant rings.- 7.1 Coherent and reduced rings.- 7.2 Invariant rings.- 7.3 Rings with integrally closed factor rings.- 8 Endomorphism rings.- 8.1 Modules over endomorphism rings and quasi injective modules.- 8.2 Nilpotent endomorphisms.- 8.3 Strongly indecomposable modules.- 9 Distributive rings with maximum conditions.- 9.1 Arithmetics of ideals.- 9.2 Noel.herian rings.- 9.3 Classical rings of quotients of distributive rings.- 9.4 Rings algebraic over their centre.- 10 Self-injective and skew-injective rings.- 10.1 Quasi-frobenius rings and direct sums of injective modules.- 10.2 Cyclic ?-injective modules.- 10.3 Integrally closed Noetherian rings.- 10.4 Cyclic skew-injective modules.- 10.5 Countably injective rings.- 11 Semidistributive and serial rings.- 11.1 Semidistributive modules.- 11.2 Semidistributive rings.- 11.3 Serial modules and rings.- 12 Monoidrings and related topics.- 12.1 Series and polynomial rings.- 12.2 Quaternion algebras.- 12.3 Subgroups, submonoids, and annihilators.- 12.4 Regular group rings.- 12.5 Cancellative monoids.- 12.6 Semilattices and regular monoids.

Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.

• 1 Radicals, local and semisimple modules.- 1.1 Maximal submodules and the Jacobson radical.- 1.2 Local and uniserial modules.- 1.3 Semisimple and Artinian modules.- 1.4 The prime radical.- 2 Projective and injective modules.- 2.1 Free and projective modules.- 2.2 Injective modules.- 2.3 Injective hull.- 3 Bezout and regular modules.- 3.1 Regular modules.- 3.2 Unit-regular rings.- 3.3 Semilocal rings and distributivity.- 3.4 Strongly regular rings.- 3.5 Bezout rings.- 4 Continuous and finite-dimensional modules.- 4.1 Closed submodules.- 4.2 Continuous modules.- 4.3 Finile-dimensional modules.- 4.4 Nonsingular ?-injective modules.- 5 Rings of quotients.- 5.1 Ore sets.- 5.2 Denominator sets and localizable rings.- 5.3 Maximal rings of quotients.- 6 Flat modules and semiperfect rings.- 6.1 Characterizations of flat modules.- 6.2 Submodules of flat modules.- 6.3 Semiperfect and perfect rings.- 7 Semihereditary and invariant rings.- 7.1 Coherent and reduced rings.- 7.2 Invariant rings.- 7.3 Rings with integrally closed factor rings.- 8 Endomorphism rings.- 8.1 Modules over endomorphism rings and quasi injective modules.- 8.2 Nilpotent endomorphisms.- 8.3 Strongly indecomposable modules.- 9 Distributive rings with maximum conditions.- 9.1 Arithmetics of ideals.- 9.2 Noel.herian rings.- 9.3 Classical rings of quotients of distributive rings.- 9.4 Rings algebraic over their centre.- 10 Self-injective and skew-injective rings.- 10.1 Quasi-frobenius rings and direct sums of injective modules.- 10.2 Cyclic ?-injective modules.- 10.3 Integrally closed Noetherian rings.- 10.4 Cyclic skew-injective modules.- 10.5 Countably injective rings.- 11 Semidistributive and serial rings.- 11.1 Semidistributive modules.- 11.2 Semidistributive rings.- 11.3 Serial modules and rings.- 12 Monoidrings and related topics.- 12.1 Series and polynomial rings.- 12.2 Quaternion algebras.- 12.3 Subgroups, submonoids, and annihilators.- 12.4 Regular group rings.- 12.5 Cancellative monoids.- 12.6 Semilattices and regular monoids.