ABSTRACT
This chapter represents the properties and structure of various classes of rings whose lattices of submodule are distributive. It presents properties of and the structure results for semiperfect semidistributive rings (SPSD-rings). The chapter considers some important properties of distributive modules and rings. It discusses the structure of Noetherian distributive and semidistributive rings. The chapter provides some further characterization of distributive rings in terms of ideals. Recall that a module is called semidistributive if it is a direct sum of distributive modules. A ring is distributive if it both right and left distributive. The class of distributive modules includes the class of all simple and all uniserial modules. The chapter considers a special class of semihereditary rings; namely semiperfect semidistributive rings. It describes special classes of semiperfect semidistributive rings, namely right hereditary SPSD-rings. Commutative distributive rings are also called arithmetical rings.
