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A *-ring R is called a nil *-clean ring if every element of R is a sum of a projection and a nilpotent.Nil *-clean rings are the *-version of nil-clean rings introduced by Diesl.This paper is about the nil *-clean property of rings with emphasis on matrix rings.We show that a *-ring R is nil *-clean if and only if J(R) is nil and R/J(R) is nil*-clean.For a 2-primal *-ring R,with the induced involution given by (aij)* =(a*ij)T,the nil *-clean property of Mn(R) is completely reduced to that of Mn(Z2).Consequently,Mn(R) is not a nil *-clean ring for n =3,4,and M2(R) is a nil *-clean ring if and only if J(R) is nil,R/J(R) is a Boolean ring and a*-a ∈ J(R) for all a ∈ R. 相似文献
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We construct the Grothendieck rings of a class of 2n2dimensional semisimple Hopf Algebras H2n2,which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H8.All irreducible H2n2-modules are classified.Furthermore,we describe the Grothendieck rings r(H2n2)by generators and relations explicitly. 相似文献
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A detailed study of the geometry, aromatic character, electronic and magnetic properties for a series of positively charged N-doped polycyclic aromatic hydrocarbons (PAHs) was performed. Magnetic properties of the examined molecules were analyzed by means of the magnetically induced current density calculated using the diamagnetic-zero version of the continuous transformation of origin of current density (CTOCD-DZ) method. The comparative study of the local aromaticity of the studied molecules was performed using several different indices: energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six centre delocalization index (SCI) and nucleus independent chemical shifts (NICS). The presence of N-atoms in the inner rings was found to cause a planarity distortion in the studied N-doped systems. The geometric changes and charged nature of the studied N-doped systems do not significantly influence the current density and the local aromaticity distribution in comparison with the corresponding parent benzenoid hydrocarbons. The present study demonstrates how quantum chemical calculations can be used for rational design of novel PAHs and for fine tuning of their properties. 相似文献
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We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation. Compared with previous results, the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling. With the modulation of the spin–orbit coupling, not only the lifetime of ring dark solitons is greatly prolonged, but also their attenuation kinetics is significantly affected. For two shallow ring dark solitons with the equal strength of the spin–orbit coupling, the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value. Due to the effect of the snake instability, ring dark solitons split into a series of ring-like clusters of vortex pairs, which perform complex oscillations. This indicates that the system is strongly dependent on the presence of the spin–orbit coupling. Furthermore, the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(4):106862
We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated. 相似文献
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We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the assumption that the abelian surface does not contain low genus curves. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization. 相似文献
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