in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

In this paper, we construct subring homomorphic encryption scheme that is a homomorphic encryption scheme built on the decomposition ring, which is a subring of cyclotomic ring. In the scheme, each plaintext slot contains an integer in Zpl , rather than an element of GF(p) as in conventional homomorphic encryption schemes on cyclotomic rings. Our benchmark results indicate that the subring homo...

A minimum depth is assigned to a ring homomorphism and a bimodule over its codomain. When the homomorphism is an inclusion and the bimodule is the codomain, the recent notion of depth of a subring in a paper by Boltje-Danz-Külshammer is recovered . Subring depth below an ideal gives a lower bound for BDK’s subring depth of a group algebra pair or a semisimple complex algebra pair.

1-2. (a) Let u, v ∈ S and suppose that uv = 0; then u = 0 or v = 0 since u, v ∈ R and R is an integral domain. Consider the unit homomorphisms η : Z −→ R and η′ : Z −→ S. Then for n ∈ Z, η′(n) = η(n), so ker η′ = ker η and therefore charS = charR. (b) Q is a field and Z ⊆ Q is a subring which is not a field. 1-3. (a) For any subring R ⊆ C, R is an integral domain with characteristic subring Z a...

<p>In this paper, we define the - -fuzzy subring and discussed various fundamental aspects of subrings. We introduce concept -level subset new fuzzy set prove that form a ring. ideal show all cosets Moreover, investigate properties homomorphic image subring.</p>