in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

This paper shows how several ring-LWE based key exchange protocols can be broken, under the assumption that the same key share is used for multiple exchanges. This indicates that, if these key exchange protocols are used, then it will be necessary for a fresh key share be generated for each exchange, and that these key exchange protocols cannot be used as a drop in replacement for designs which...

in this paper, we introduce a class of $j$-quasipolar rings. let $r$ be a ring with identity. an element $a$ of a ring $r$ is called {it weakly $j$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $j(r)$ and the ring $r$ is called {it weakly $j$-quasipolar} if every element of $r$ is weakly $j$-quasipolar. we give many characterizations and investiga...

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

We study the impact of trimerization (breathing) nearest-neighbor (NN) exchange on planar XY spin-1/2 ferromagnet kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered into Z2 quantum spin liquid by virtue Using Monte-Carlo calculations, based stochastic series expansion, we present result...