… Let R be a commutative ring with nonzero identity and M a … Moreover, we characterize strongly
dccr* in terms of some … ⋆ if and only if R satisfies (C) property and dim R = 0 (see Corollary …

… Throughout this article, we consider only commutative rings with nonzero identity and nonzero
unital modules. The … Now, we characterize modules satisfying dccr in terms of modules …

… is finding finite non-group non-commutative semigroups for which dcr achieves the maximum
value. In this paper, we prove that for a non-group regular quasi-commutative semigroup S, …

… If A is a commutative local ring, we will denote by mA its maximal ideal. If A is a commutative
ring … If k is a characteristic 0 field and R is a commutative k-algebra, we will say x 2 SpecR is …

… , after doing a formal analysis of the containment-division condition, the concept of DCR is
very … of an ideal of a commutative ring with unity (with the collection of all possible ideals of this …

… Throughout this paper, R will denote a commutative ring with a … characterize Artinian rings
in terms of representable rings. … M is completely representable if and only if M satisfies (dccr) . …

… general commutative ground rings; the second part [6] focuses mostly on purely infinite simple
unital algebras over a field. We fix a commutative ring … Let ` be a ground ring satisfying the …

… vectors m ∈ R ℓ , where R is a commutative ring; and functional decryption keys sk k , derived
… Our DCR scheme is slightly faster than the HS M CL one, but less compact. Precisely for a …

… ring is commutative whenever so is the range of the derivation ı. We also provide a few useful
observations on ı-prime rings, … things a useful characterization of ı-prime rings in terms of …

… -exponent variant of the DCR assumption. A theoretical analysis of our instantiations suggest
… Note that our FSS also works polynomials over non-commutative rings. For details, refer to …