Primeness Conditions on the Lattice of Hereditary Pretorsion Classes

References

• Anderson , F. W. and Fuller , K. R. 1975 . Rings and Categories of Modules , 2nd ed. Graduate Texts in Mathematics Series 13 New York, Heidelberg, Berlin : Springer-Verlag .
   Google Scholar
• Beachy , J. A. and Blair , W. D. 1978 . Finitely annihilated modules and orders in artinian rings . Comm. Algebra , 6 ( 1 ) : 1 – 34 .
   Google Scholar
• Bican , L. , Kepka , T. and Nĕmec , P. 1982 . Rings, Modules and Preradicals , Lecture Notes in Pure and Applied Mathematics Series 75 New York : Marcel Dekker .
   Google Scholar
• Golan , J. S. 1987 . Linear Topologies on a Ring: An Overview , Pitman Research Notes in Mathematics Series 159 Harlow : Longman Scientific and Technical .
   Google Scholar
• Raggi , F. , Rìos Montes , J. and Wisbauer , R. 2001 . The lattice structure of hereditary pretorsion classes . Comm. Algebra , 29 ( 1 ) : 131 – 140 .
   Google Scholar
• Stenström , B. 1975 . Rings of Quotients , Grundlehren Mathematischen Wissenschaften Series 237 New York, Heidelberg, Berlin : Springer-Verlag .
   Google Scholar
• van den Berg , J. E. 1999 . When multiplication of topologizing filters is commutative . J. Pure Applied Algebra , 140 : 87 – 105 .
   Google Scholar
• van den Berg , J. E. 2002 . Primeness described in the language of torsion preradicals . Semigroup Forum , 64 : 425 – 442 .
   Google Scholar
• #Communicated by E. Puczyłowski.
   Google Scholar
• aStrictly speaking, the embedding of Id R in ptors R is order reversing. For this reason if Id R is to be viewed as a substructure of ptors R, and this is the perspective we shall offer, then the order relation on Id R must be taken to be reverse set inclusion.
   Google Scholar