We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's real quaternions. also characterize generalized identities which hold quaternions, and more generally, any division algebra .

Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E∞-ring spectrum, based on the study of elliptic curves with level-3 structure. We show that the natural map forgetting this level structure induces an E∞-ring map from the spectrum of topological modular forms to this truncated Brown-Peterson spectrum, and that this orientation ...

In this paper a generalized version of the Bass formula is proved for finitely generated modules of finite Gorenstein injective dimension over a commutative noetherian ring.

In this paper, we prove the generalized Hyers–Ulam stability of homomorphisms and (θ, φ)-derivations on a ring R into a Banach R-bimodule M.

In this paper we study the vanishing and non-vanishing of generalized local cohomology and generalized local homology. In particular for a Noetherian local ring (R,m) and two non-zero finitely generated R-modules M and N , it is shown that H m (M,N) 6= 0.

We resolve an open problem in commutative algebra and Field Arithmetic, posed by Jarden – Let R be a generalized Krull domain. Is the ring R[[X]] of formal power series over R a generalized Krull domain? We show that the answer is negative.

In this paper we study generalized Reed-Solomon codes (GRS codes) over commutative, noncommutative rings, show that the classical Welch-Berlekamp and Guruswami-Sudan decoding algorithms still hold in this context and we investigate their complexities. Under some hypothesis, the study of noncommutative generalized Reed-Solomon codes over finite rings leads to the fact that GRS code over commutat...

In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...

The injection line and main ring lattice designs for the University of Maryland Electron Ring [1] have been studied numerically. Possible injection systems were designed using a fitting algorithm based on a set of generalized rms-envelope equations that include the effects of space charge and beam momentum dispersion. The beam dynamics of the injection into and through the periodical ring struc...

Abstract We investigate special points on the Grassmannian, which correspond to friezes with coefficients in case of rank two. Using representations arithmetic matroids, we obtain a theorem subpolygons specializations coordinate ring. As case, recover characterization classic frieze patterns. Moreover, observe that specializing clusters ring Grassmannian units yields may be interpreted as arran...