Defect And Radicals Of Δ-Endomorphism Near-Rings
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
We investigate -directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids...
A semiring S in 𝕊𝕃⁺ is a t-k-Archimedean semiring if for all a,b ∈ S, b ∈ √(Sa) ∩ √(aS). Here we introduce the t-k-Archimedean semirings and characterize the semirings which are distributive lattice (chain) of t-k-Archimedean semirings. A semiring S is a distributive lattice of t-k-Archimedean semirings if and only if √B is a k-ideal, and S is a chain of t-k-Archimedean semirings if and only if √B is a completely prime k-ideal, for every k-bi-ideal B of S.