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Idealiser Rings of Injective Dimension One
Preview AbstractWe study a certain type of prime Noetherian idealiser ring R of injective dimension 1, and prove for instance that the idempotent ideals of R are projective and that every non-zero projective ideal of R is uniquely of the form UE for some invertible ideal U and idempotent ideal E of R. Formulae are given for the number of idempotent ideals of R and the number of orders which contain R.
Prime Ideals in Group Near-rings
Preview AbstractThe flow (or lack thereof) of several kinds of primeness between a zero-symmetric near-ring R and its group near-ring R[G] for certain groups G is discussed. In certain cases, results are contrasted against what happens in the matrix near-ring situation.