TY - JOUR

T1 - Superfluous ideals of N-groups

AU - Rajani, S.

AU - Tapatee, S.

AU - Harikrishnan, P.

AU - Kedukodi, B. S.

AU - Kuncham, S. P.

N1 - Funding Information:
The authors thank the referees for their valuable comments. Author acknowledges Dr. T M A Pai Fellowship, MAHE, Manipal. All the authors acknowledge Manipal Institute of Technology (Manipal/Bengaluru), Manipal Academy of Higher Education for the kind encouragement.
Publisher Copyright:
© 2023, The Author(s).

PY - 2023/12

Y1 - 2023/12

N2 - We consider a right nearring N and a module over N (known as, N-group). For an arbitrary ideal (or N-subgroup) Ω of an N-group G, we define the notions Ω-superfluous, strictly Ω-superfluous, g-superfluous ideals of G. We give suitable examples to distinguish between these classes and the existing classes studied in Bhavanari (Proc Japan Acad 61-A:23–25, 1985; Indian J Pure Appl Math 22:633–636, 1991; J Austral Math Soc 57:170–178, 1994), and prove some properties. For a zero-symmetric nearring with 1, we consider a module over a matrix nearring and obtain one-one correspondence between the superfluous ideals of an N-group (over itself) and those of Mn(N) -group Nn, where Mn(N) is the matrix nearring over N. Furthermore, we define a graph of superfluous ideals of a nearring and prove some properties with necessary examples.

AB - We consider a right nearring N and a module over N (known as, N-group). For an arbitrary ideal (or N-subgroup) Ω of an N-group G, we define the notions Ω-superfluous, strictly Ω-superfluous, g-superfluous ideals of G. We give suitable examples to distinguish between these classes and the existing classes studied in Bhavanari (Proc Japan Acad 61-A:23–25, 1985; Indian J Pure Appl Math 22:633–636, 1991; J Austral Math Soc 57:170–178, 1994), and prove some properties. For a zero-symmetric nearring with 1, we consider a module over a matrix nearring and obtain one-one correspondence between the superfluous ideals of an N-group (over itself) and those of Mn(N) -group Nn, where Mn(N) is the matrix nearring over N. Furthermore, we define a graph of superfluous ideals of a nearring and prove some properties with necessary examples.

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U2 - 10.1007/s12215-023-00888-2

DO - 10.1007/s12215-023-00888-2

M3 - Article

AN - SCOPUS:85153406855

SN - 0009-725X

VL - 72

SP - 4149

EP - 4167

JO - Rendiconti del Circolo Matematico di Palermo

JF - Rendiconti del Circolo Matematico di Palermo

IS - 8

ER -