Primes and G-primes in $$\mathbb {Z}$$-nearalgebras

Abstract Let N be a $$\mathbb {Z}$$ Z -nearalgebra; that is, left nearring with identity satisfying $$ k(nn^{\prime })=(kn)n^{\prime }=n(kn^{\prime })$$ k ( n ′ ) = for all $$k\in \mathbb ∈ , $$n,n^{\prime }\in N$$ , N and G finite group acting on . Then the skew $$N*G$$ ∗ G of over is formed. If 3-prime ( $$aNb=0$$ a b 0 implies $$a=0$$ or $$b=0$$ ), then quotients Q_{0}(N)$$ Q constructed using semigroup ideals $$A_{i}$$ A i (a multiplicative closed set $$A_{i}\subseteq ⊆ such $$A_{i}N\subseteq A_{i}\supseteq NA_{i}$$ ⊇ ) maps $$f_{i}:A_{i}\rightarrow f : → (na)f_{i}=n(af_{i})$$ $$n\in $$a\in A_{i}$$ Through $$Q_{0}(N)$$ we discuss relationships between invariant prime subnearrings I -primes) -invariant GI Particularly describe -primes $$P_{i}$$ P each P_{i}\cap N=\{0\}$$ ∩ { } -prime As an application, settle Incomparability Going Down Problem in this situation.