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Öğe On 2-absorbing primary and weakly 2-Absorbing elements in multiplicative lattices(Forum-Editrice Universitaria Udinese SRL, 2015) Çallialp F.; Yetkin E.; Tekir U.In this paper, we introduce the concept of 2-absorbing primary and weakly 2-absorbing primary elements which are generalizations of primary and weakly primary elements in multiplicative lattices. Let L be a multiplicative lattice. A proper element q of L is said to be a (weakly) 2-absorbing primary element of L if whenever a,b,c ? L with (0 ? abc ? q) abc ? q implies either ab ? q or ac ? ?q or bc ? ?q. Some properties of 2-absorbing primary and weakly 2-absorbing primary elements are presented and relations among prime, primary, 2-absorbing, weakly 2-absorbing, 2-absorbing primary and weakly 2-absorbing primary elements are investigated. Furthermore, we determine 2-absorbing primary elements in some special lattices and give a new characterization for principal element domains in terms of 2-absorbing primary elements.
