The concept of the Jacobson radical of a ring is generalized to semirings. A semiring is a system consisting of a set S together with two binary operations, called addition and multiplication, which forms a semigroup relative to addition, a semigroup relative to multiplication, and the right and left distributive laws hold. The additive semigroup of S is assumed to be commutative. The right ide...

We develop an approach to utilize anisotropic metamaterials to solve one of the fundamental problems of modern plasmonics--parasitic scattering of surface waves into free-space modes, opening the road to truly two-dimensional plasmonic optics. We illustrate the developed formalism on the examples of plasmonic refractor and plasmonic crystal, and discuss limitations of the developed technique an...

employed, confining himself to those which he had personally found best and adding brief accounts of other accepted methods. Unusually full reports of interesting cases were always a feature of the book, whilst the needs of candidates for the higher examinations were catered for in detailed descriptions of amputations, ligation of arteries and other operations which figure more prominently in t...

1.1. Strictly Cyclic Modules and Modular Right Ideals. For a ring A with identity, cyclic modules are precisely those of the form a\A where a is a right ideal. What might be a useful analogous statement for a ring without identity? This question motivates what follows in this subsection. A module M is strictly cyclic if there exists m in M such that mA = M (such an m is called a generator); a r...