The motivation of this article is to define approximately near rings, some types $N$-groups, ideals, and rings all descriptive cosets. Moreover, properties these algebraic structures are given. Furthermore, near-ring homomorphisms introduced their investigated.

In many real-world auctions, a bidder does not know her exact value for an item, but can perform costly deliberation to reduce uncertainty. Relatively little is known about such deliberative environments, which are fundamentally different from classical auction environments. this paper, we propose new approach that allows us leverage revenue-maximization results in particular, use Myerson (1981...