View More View Less
  • 1 Please ask the editor of the journal.
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Beside near-rings with zero-multiplication or constant multiplication also other near- rings can be considered as near-rings with trivial multiplication. From a structure theoret- ical point of view it is reasonable to consider Kurosh{Amitsur radical classes which contain all near-rings with trivial multiplication. In the present note, continuing the investigations of [2], [4] and [5], we shall characterize the semisimple classes of such radical classes. Our characterizations look clumsier than those in [2], [4] and [5], but we exhibit that exact analogues of the mentioned characterizations cannot be achieved.

  • VELDSMAN, S., Hereditary conditions on classes of near-rings, Studia Sci. Math. Hungar. 23 (1988), 411-415. MR 89k:16072

    'Hereditary conditions on classes of near-rings ' () 23 Studia Sci. Math. Hungar. : 411 -415.

    • Search Google Scholar
  • MLITZ, R. and WIEGANDT, R., Semisimple classes of hypernilpotent and hyperconstant near-ring radicals, Arch. Math. (Basel) 63 (1994), 414-419. MR 95i:16050

    'Semisimple classes of hypernilpotent and hyperconstant near-ring radicals ' () 63 Arch. Math. (Basel) : 414 -419.

    • Search Google Scholar
  • PILZ, G., Near-rings, North-Holland Mathematics Studies, 23, North-Holland Publishing Co., Amsterdam-New York, 1983. MR 85h:16046

    23

  • VELDSMAN, S., Supernilpotent radicals of near-rings, Comm. Algebra 15 (1987), 2497-2509. MR 88j:16049

    'Supernilpotent radicals of near-rings ' () 15 Comm. Algebra : 2497 -2509.

  • VELDSMAN, S., Near-ring radicals with hereditary semisimple classes, Arch. Math. (Basel) 54 (1990), 443-447. MR 91b:16055

    'Near-ring radicals with hereditary semisimple classes ' () 54 Arch. Math. (Basel) : 443 -447.

    • Search Google Scholar
  • MALONE, J. J., Near-rings with trivial multiplications, Amer. Math. Monthly 74 (1967), 1111-1112. MR 37 #1416

    'Near-rings with trivial multiplications ' () 74 Amer. Math. Monthly : 1111 -1112.