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# Peter Fuchs

* Peter Fuchs *
(Back to Team Overview)

a. Univ.-Prof. Dipl.-Ing. Dr.

S2 0369

Phone: +43 732 2468 6859

office hours: Monday: 10:15-12:00

peter.fuchs(/\t)jku.at

Completed his Doctoral Thesis in 1985, entitled "Ultraproducts of 1/2-groups" and later made his Habilitation in 1994. Peter is interested in many areas of abstract algebra, including ring theory, matrix theory, coding theory and nearrings.

He has gone on to publish over thirty papers, collaborating with many people in the process.

"The role of filters for describing substructures of transformation near- rings", Institutsber. No. 278, 1984, Univ. Linz, Austria

"Ultraproducts of 1/2-groups", Diss. Univ. Linz, Austria, 1985. mr 89e-03046.

"On the ideal structure in ultraproducts of affine near-rings", in ``Near-Rings and Near-Fields'' (ed.: G.~Betsch), North-Holland, Amsterdam 1987, 79-86. mr 88c-16048.

"Isomorphisms between lattices of filters and lattices of substructures in transformation near-rings", manuscript

"On near-rings in which the constants form an ideal", Bull. Austral. Math. Soc. 39 (1989), 171-175. mr 90e-16059.

"On function algebras in which every congruence is determined by a filter", J. Pure and Appl. Algebra 67 (1990), 259-267. mr 92b-08002.

"On pseudo-finite near-fields which have finite dimension over the center", Proc. Edinb. Math. Soc. 32 (1989), 371-375. mr 90h-12014.

"On the structure of ideals in sandwich near-rings", Results in Math. 17 (1990), 256-271. mr 91e-16054.

"A decoding method for planar near-ring codes", Riv. Mat. Univ. Parma (4) 17. (1991), 325-331. mr 93g-16055.

"A characterisation result for matrix rings", Bull. Austral. Math. Soc. 43 (1991), 265-267.

"On the construction of codes by using composition", in: Contrib. Gen. Alg. 8 (ed.: G.Pilz), Hölder-Pichler-Tempsky, Vienna and Teubner, Stuttgart, 1992, 71-80.

with HOFER, Gerhard and PILZ, Günter "Codes from planar near-rings", IEEE Trans. on Information Theory 36 (1990), 647-651. mr 91b-94028

with MAXSON, Carlton J.

"Kernels of covered groups with operators", J. of Algebra 114 (1988), 68-80. mr 89e-20046

"Near-fields associated with invariant linear $\kappa$-relations", Proc. Amer. Math. Soc. 103 (1988), 729-736. mr 89f-16053.

"Meromorphic products determining near-fields", J. Austral. Math. Soc. A 46 (1989), 365-370. mr 90e-12022

"Centralizer near-rings determined by PID-modules", Arch. Math. 56 (1991), 140-147. mr 92a-16052.

"Rings of homogeneous functions determined by Artinian ring module", J.of Algebra, to appear.

with KABZA, Lucyna "On the simplicity of non-zerosymmetric near-rings over meromorphic products" Communications in Algebra, to appear.

with MAXSON, Carlton J. and PILZ, Günter F. "On rings for which homogeneous maps are linear", Proc. Amer. Math. Soc. 112 (1991), 1-7. mr 91h-16054.

with MAXSON, Carlton J. and SMITH, K.C. "Centralizer near-rings determined by unions of groups", Result. Math. 11 (1987), 198-210. mr 88j-16046.

with MAXSON, Carlton J., VAN DER WALT, Andries P.J. and KAARLI, Kalle "Centralizer near-rings determined by PID-modules, II", Periodica Math. Hung. 26 (2) (1993), 111-114.

with MAXSON, C.J., PETTET, M.R. and SMITH, K.C "Centralizer near-rings determined by fixed point free automorphism groups", Proc. Royal Soc. of Edinburgh 107 A (1987), 327-337. mr 89a-16051.

with PILZ, Günter

"Ultraproducts and ultralimits of near-rings", Monatsh. Math. 100 (1985), 105-112. mr 87j-16016.

"A new density theorem for primitive near-rings", submitted