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- W2115565662 abstract "For near-ring ideal mappings ρ 1 and ρ 2 , we investigate radical theoretical properties of and the relationship among the class pairs (ρ 1 : ρ 2 ), [Formula: see text] and (ℛ ρ 2 : ℛ ρ 1 ). Conditions on ρ 1 and ρ 2 are given for a general class pair to form a radical class of various types. These types include the Plotkin and KA-radical varieties. A number of examples are shown to motivate the suitability of the theory of Hoehnke-radicals over KA-radicals when radical pairs of near-rings are studied. In particular, it is shown that [Formula: see text] forms a KA-radical class, where [Formula: see text] denotes the class of completely prime near-rings and [Formula: see text] the class of 3-prime near-rings. This gives another near-ring generalization of the 2-primal ring concept. The theory of radical pairs are also used to show that in general the class of 3-semiprime near-rings is not the semisimple class of the 3-prime radical." @default.
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- W2115565662 date "2005-03-01" @default.
- W2115565662 modified "2023-09-27" @default.
- W2115565662 title "Near-Ring Radicals and Class Pairs" @default.
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- W2115565662 doi "https://doi.org/10.1142/s100538670500009x" @default.
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