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 -