Commutative algebra, expansions of ideals of commutative rings

1. Gulsen Ulucak, Suat Koc, Unsal Tekir, “On n-1-absorbing prime ideals”, In this paper, we introduce and study n-1-absorbing prime ideals of commutative rings. Let R be a ring and na positive integer. A proper ideal I of R is said to be an n-1-absorbing prime ideal if whenever x1x2··· xn+ 1∈ I for some nonunits x1, x2,..., xn+ 1∈ R, then either x1x2··· xn∈ I or xn+ 1∈ I. It is obvious that 1-1-absorbing (2-1-absorbing) prime ideals are exactly prime (1-absorbing prime) ideals. Various examples and characterizations of n-1-absorbing prime ideals are given., Journal of Algebra and its Applications, 2023
2. Gulsen Ulucak, Unsal Tekir, Suat Koç, “On S-2-absorbing submodules and vn-regular modules”, Let R be a commutative ring and M an R-module. In this article, we introduce the concept of S-2-absorbing submodule. Suppose that S⊆ R is a multiplicatively closed subset of R. A submodule P of M with (P: R M)∩ S=∅ is said to be an S-2-absorbing submodule if there exists an element s∈ S and whenever abm∈ P for some a, b∈ R and m∈ M, then sab∈(P: R M) or sam∈ P or sbm∈ P. Many examples, characterizations and properties of S-2-absorbing submodules are given. Moreover, we use them to characterize von Neumann regular modules in the sense [9]., An. St. Univ. Ovidius Constanta, 2:28 (2020)
3. Kar Ping Shum, Gulsen Ulucak, Ünsal Tekir, Suat Koç, “On principal element lattices”, In this paper, we study principal element lattices, Prüfer lattices and Q-lattices. Also, a necessary and sufficient condition is given for a principally generated C-lattice to be a finite direct product of proper Dedekind domains., Algebra universalis, 2:82 (2021)

• Gebze Technical University