primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...

The influence of the martensitic, martensitic+austenitic and austenitic structures in bending training on two-way shape memory effect (TWSME) in Ni-50.8 at %Ti and Ni-49.9 at %Ti alloys was studied. In addition of the primary structure, the effect of pre-strain, plastic strain, training cycle and training temperature on the TWSME was investigated. The prepared samples were trained in martensiti...

let r be a commutative ring and m be an r-module. we say that m is fully primary, if every proper submodule of m is primary. in this paper, we state some characterizations of fully primary modules. we also give some characterizations of rings over which every module is fully primary, and of those rings over which there exists a faithful fully primary module. furthermore, we will introduce some ...