• 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.
Keywords
ring, Fields, near – ring, near-field, amalgamated duplication, generically Cohen-Macaulay near-field, generically Gorenstein near-field, approximately Cohen-Macaulay near-field, approximately Gorenstein near-field.
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