A ring $R$ is called right (small) dual if every (small) right ideal of $R$ is a right annihilator. Left (small) dual rings can be defined similarly. And a ring $R$ is called (small) dual if $R$ is left and right (small) dual. It is proved that $R$ i...
Let $R$ be a finite ring with identity. The clean graph $Cl(R)$ of a ring $R$ is a graph whose vertices are pairs $(e, u)$, where $e$ is an idempotent element and $u$ is a unit of $R$. Two distinct vertices $(e, u)$ and $(f, v)$ are adjacent if and o...
In this paper, we introduce a strong property $(A)$ and we study the transfer of property $(A)$ and strong property $(A)$ in trivial ring extensions and amalgamated duplication of a ring along an ideal. We also exhibit a class of rings which satisf...
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In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give equivalent conditions for SIP and SSP modules; establish connections between the class of semisimple artinian rings and the class of SIP rings. It shows that $R...
ELDEN RING update 1.12 is now available. This is also a Day One Patch that enables players to play Shadow of the Erdtree (when it releases). ## New feature * Added support for the **SHADOW OF THE E...
co-wrote Mabel's hit singles "Finders Keepers" and "Fine Line", as well as the Not3s single "My Lover" and Jax Jones' hit "Ring Ring". He has also co-written
In this paper we study the commutativity of the Frobenius functor and the colon operation of two ideals for Noetherian rings of positive characteristic $p$. New characterizations of regular rings and local UFDs are given....
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A ring is clean (resp. almost clean) if each of its elements is the sum of a unit (resp. regular element) and an idempotent. In this paper we define the analogous notion for *-rings: a *-ring is *-clean (resp. almost *-clean) if its every element is...
Vortex machine may refer to: Vortex ring gun, a weapon Vortex ring toy Air vortex cannon, a toy Vortex tube, a device for separating gases by temperature
A vortex ring, also called a toroidal vortex, is a torus-shaped vortex in a fluid; that is, a region where the fluid mostly spins around an imaginary axis