TY - JOUR

T1 - On completely 2-absorbing ideals of N-groups

AU - Sahoo, Taptee

AU - Deepak Shetty, M.

AU - Groenewald, N. J.

AU - Harikrishnan, P. K.

AU - Kuncham, S. P.

N1 - Publisher Copyright:
© 2021 Taru Publications.

PY - 2021

Y1 - 2021

N2 - We introduce the notion of completely 2-absorbing (denoted by, c-2-absorbing) ideal of an N-group G, as a generalization of completely prime ideal of module over a right near-ring N. We obtain that, for an ideal I of a monogenic N-group G, if (I: G) is a c-2-absorbing ideal of N, then I is a c-2-absorbing ideal of G. The converse also holds only when G is locally monogenic over a distributive near-ring N. We discuss the properties such as homomorphic images, inverse images of c-2-absorbing ideals of G. Examples of c-2-absorbing ideals of N-groups are given where N is non-commutative and in the sequel some results of 2-absorbing ideals from module over rings are generalized to N-groups.

AB - We introduce the notion of completely 2-absorbing (denoted by, c-2-absorbing) ideal of an N-group G, as a generalization of completely prime ideal of module over a right near-ring N. We obtain that, for an ideal I of a monogenic N-group G, if (I: G) is a c-2-absorbing ideal of N, then I is a c-2-absorbing ideal of G. The converse also holds only when G is locally monogenic over a distributive near-ring N. We discuss the properties such as homomorphic images, inverse images of c-2-absorbing ideals of G. Examples of c-2-absorbing ideals of N-groups are given where N is non-commutative and in the sequel some results of 2-absorbing ideals from module over rings are generalized to N-groups.

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U2 - 10.1080/09720529.2021.1892268

DO - 10.1080/09720529.2021.1892268

M3 - Article

AN - SCOPUS:85104241924

VL - 24

SP - 541

EP - 556

JO - Journal of Discrete Mathematical Sciences and Cryptography

JF - Journal of Discrete Mathematical Sciences and Cryptography

SN - 0972-0529

IS - 2

ER -