TY - GEN

T1 - Generalized Essential Submodule Graph of an. R-module

AU - Salvankar, Rajani

AU - Kedukodi, Babushri Srinivas

AU - Panackal, Harikrishnan

AU - Kuncham, Syam Prasad

N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023.

PY - 2023

Y1 - 2023

N2 - Let. M be a finitely generated left module over a ring. R with 1. We introduce generalized essential submodule graph, denoted as.g-EM. We show that every maximal submodule is a universal vertex of.g-EM; consequently, we prove that the graph is connected with diameter at most 2. Furthermore, we define a proper.g-essential submodule graph and prove the existence of a path between every two small submodules. We compute the.g-essential submodule graph of the.Z-module.Zn for different values of.n and obtain some properties.

AB - Let. M be a finitely generated left module over a ring. R with 1. We introduce generalized essential submodule graph, denoted as.g-EM. We show that every maximal submodule is a universal vertex of.g-EM; consequently, we prove that the graph is connected with diameter at most 2. Furthermore, we define a proper.g-essential submodule graph and prove the existence of a path between every two small submodules. We compute the.g-essential submodule graph of the.Z-module.Zn for different values of.n and obtain some properties.

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U2 - 10.1007/978-981-99-6349-2_8

DO - 10.1007/978-981-99-6349-2_8

M3 - Conference contribution

AN - SCOPUS:85188879787

SN - 9789819963485

T3 - Springer Proceedings in Mathematics and Statistics

SP - 149

EP - 158

BT - Semigroups, Algebras and Operator Theory - ICSAOT 2022

A2 - Ambily, A.A.

A2 - Kiran Kumar, V.B.

PB - Springer

T2 - International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022

Y2 - 28 March 2022 through 31 March 2022

ER -