id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-3900	S.Sivanthi	Some Special Structures of〖 δ〗_1 Near-Rings	2025	8	.pdf	application/pdf	3885	278	87	[we write xy for x.y for all x, y in N] and (iii) (𝑥 + 𝑦)𝑧 = 𝑥𝑧 + 𝑦𝑧 for all x, y, z in N. Because of (iii) 0n =0 for all n in N. As we do not stipulate the left distributive law, n0 = 0” need not hold good for all n in N. We say that N is zero-symmetric if 𝑛0 = 0 for all n in N. N is called an S-near-ring or an S'-near-ring according as 𝑥 ∈ 𝑁𝑥 or 𝑥 ∈ 𝑥𝑁 for all 𝑥 ∈ 𝑁. A subgroup M of N is called an Nsubgroup if 𝑁𝑀 ⊂ 𝑀 and an invariant N-subgroup if, in addition, 𝑀𝑁 ⊂ 𝑀. An ideal I of N is called a semi prime ideal if for all ideals J of N. 𝐽2 ⊂ 𝐼 ⇒ 𝐽 ⊂ 𝐼 . Now 𝑥2 ∈ 𝑥𝑁 for all x in N ⇒ 𝑥2 ∈ 𝑁𝑥2	cache/cana-3900.pdf	txt/cana-3900.txt