• AMALGAMATED DUPLICATION OF SOME SPECIAL NEAR-FIELDS (AD-SP-N-F)

Abstract

In this paper I study and introducing myself some special type of near – fields amalgamated duplication near-field N ⋈ I over the rings and near-rings N. After in depth study of amalgamated duplication of some special rings achieved by D’Ama and Fontana. Let N be a commutative Noetherian near-filed and let I be an ideal of N. It is shown that if N is generically Cohen-Macaulay (resp. generically Gorenstein) and I is generically maximal Cohen-Macaulay (resp. generically canonical module), the N ⋈ I is generically Cohen-Macaulay (resp. generically Gorenstein). We also generically quasi – Gorenstein near-field and we investigate when N ⋈ I is generically quasi – Gorenstein near-field. In addition, it is shown that N ⋈ I is approximately Cohen-Macaulay if and only if N is approximately Cohen-Macaulay, provided some special conditions. Finally, it is shown that if N is approximately Gorenstein, then N ⋈ I is approximately Gorenstein.