Generalized supplemented lattices

Bicer, Cigdem; Nebiyev, Celil; Pancar, Ali

doi:10.18514/mmn.2018.1974

Cited by 3 publications

(2 citation statements)

References 6 publications

(8 reference statements)

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“…More results about (amply) supplemented modules are in [11]. The definition of generalized supplemented lattices and some important properties of them are in [6]. Some important properties of Rad− ⊕ −supplemented modules are in [4,7,10].…”

Section: Introductionmentioning

confidence: 99%

Rad−⊕−supplemented lattices

Bicer¹,

Nebiyev²

2023

MMN

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In this work, we define Rad− ⊕ −supplemented and strongly Rad− ⊕ −supplemented lattices and give some properties of these lattices. We generalize some properties of Rad− ⊕ −supplemented modules to lattices. Let L be a lattice and 1 = a 1 ⊕a 2 ⊕. . .⊕a n with a 1 , a 2 , . . . , a n ∈ L. If a i /0 is Rad− ⊕ − supplemented for every i = 1, 2, . . . , n, then L is also Rad− ⊕ − supplemented. Let L be a distributive Rad−⊕−supplemented lattice. Then 1/u is Rad−⊕−supplemented for every u ∈ L. We also define completely Rad− ⊕ −supplemented lattices and prove that every Rad− ⊕ −supplemented lattice with SSP property is completely Rad− ⊕ − supplemented.

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Section: Introductionmentioning

confidence: 99%

Rad−⊕−supplemented lattices

Bicer¹,

Nebiyev²

2023

MMN

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“…Some important properties of supplement submodules are in [8]. The definition of generalized supplemented lattices and some properties of them are in [3]. The definition ofˇ relation on lattices and some properties of this relation are in [7].…”

Section: Introductionmentioning

confidence: 99%

On supplement elements in lattices

Nebiyev¹

2019

MMN

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In this work, some properties of supplement elements in lattices are investigated. Some relation between lying above and (weak) supplement elements also studied. Some properties of supplement submodules in modules which given in [8] are generalized to lattices. Let a be a supplement of b in a lattice L. If a=0 has at least one maximal .¤ a/ element, then it is possible to define a bijective map between the maximal elements .¤ a/ of a=0 and the maximal elements .¤ 1/ of 1=b. Let a be a supplement element in a lattice L. If L is amply supplemented, then a=0 is also amply supplemented. If L is weakly supplemented, then a=0 is also weakly supplemented.

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Essential ideal of a matrix nearring and ideal related properties of graphs

Salvankar,

Babushri Srinivas,

Panackal

et al. 2024

B Soc Paran Mat

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In this paper, we consider matrix maps over a zero-symmetric right nearring $N$ with 1. We define the notions of essential ideal, superfluous ideal, generalized essential ideal of a matrix nearring and prove results which exhibit the interplay between these ideals and the corresponding ideals of the base nearring $N$. We discuss the combinatorial properties such as connectivity, diameter, completeness of a graph (denoted by $\mathcal{L}_{g}(H)$) defined on generalized essential ideals of a finitely generated module $H$ over $N$. We prove a characterization for $\mathcal{L}_{g}(H)$ to be complete. We also prove $\mathcal{L}_{g}(H)$ has diameter at-most 2 and obtain related properties with suitable illustrations.

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Generalized supplemented lattices

Cited by 3 publications

References 6 publications

Rad−⊕−supplemented lattices

Rad−⊕−supplemented lattices

On supplement elements in lattices

Essential ideal of a matrix nearring and ideal related properties of graphs

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