Relative Essential Ideals in N-groups
Let $G$ be an $N$-group where $N$ is a (right) nearring. We introduce the concept of relative essential ideal (or $N$-subgroup) as a generalization of the concept of essential submodule of a module over a ring or a nearring. We provide suitable examples to distinguish the notions relative essential and essential ideals. We prove the important properties and obtain equivalent conditions for the relative essential ideals (or $N$-subgroups) involving the quotient. Further, we derive results on direct sums, complement ideals of $N$-groups and obtain their properties under homomorphism.
Keyword(s):
2008 ◽
Vol 07
(04)
◽
pp. 507-516
◽
Keyword(s):
1994 ◽
Vol 46
(3)
◽
pp. 634-647
◽
Keyword(s):
Keyword(s):
Keyword(s):
2013 ◽
Vol 12
(05)
◽
pp. 1250208
◽