in this work, we investigate the transfer of some homological properties from a ring $r$ to its amalgamated duplication along some ideal $i$ of $r$ $rbowtie i$, and then generate new and original families of rings with these properties.

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the de nitions of n-cleanness and n-f-cleanness are equivalent.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

We define quantum determinants in matrix algebras related to pairs of compatible braidings. establish relations between these and the so-called column row determinants, which are often used theory integrable systems. also generalize spin systems using generalized Yangians demonstrate that such not uniquely determined by “quantum coordinate ring” basic space $$V$$ . For example, plane” $$xy=qyx$...

Player-Compatible Equilibrium (PCE) imposes cross-player restrictions on the magnitudes of players' “trembles” onto different strategies. These capture idea that trembles correspond to deliberate experiments by agents who are unsure prevailing distribution play. PCE selects intuitive equilibria in a number examples where trembling-hand perfect equilibrium (Selten, 1975) and proper (Myerson, 197...

Density modulations in cuprates are widely believed to be a signature of charge-density-wave (CDW) order that competes with superconductivity. Recently, we used weak-coupling approach claim these better accounted by the coexistence homogeneous d-wave gap and short-ranged pairing density waves (PDW) [1]. The full momentum dependence Bi2Sr2CaCu2O8+δ (Bi2212) was recently explored resonant inelast...