Ali ShanFA19-RMT-088LHR TP 7418Dr. Sarfraz Ahmad2026-03-162021https://repository.cuilahore.edu.pk/handle/123456789/2852The study of monomial ideal of polynomial ring ’R’ at most with the pretty clean three variables is done. The polarisation I p is known as clean If and only if, the arbitrary monomial ideal ’I’ is also relatively clean. A proper revised characterisation is prettyclean along the monomialideals in theterms of arithmetic degree is presented. This means that a simplicial complex’s polarisation corresponds to shellable if and only if a multicomplex is shellable. In this thesis Stanley decomposition with respect to prime filtrations is discussed.enDr. Sarfraz AhmadFa19MathematicsDepartment of MathematicsThesis