ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16 Y Ahmed A. M. Kamal, Cairo University, Faculty of Science, Dept. of Math. , Giza, Egypt Strongly right bounded left near-rings The aim of this paper is to introduce the concept of strongly right bounded (SRB)) to the variety of left near-rings (l. n. r.) and study some recent results concerning SRB rings for l. n. r. . We proved : - A l. n. r. R is SRB (SRB*) if and only if every nonzero right ideal (right R- subgroup) of R is an essential extension of nonzero ideal of R , moreover we characterized the largest ideal of R contained in xR for each nonzero x in the SRB* l. n. r. R.

- A l. n. r. R is SRB* if and only if the prime radical P(R) of R is SRB* ideal of R , and R contains a reduced SRB* ideal K of R such that P(R)+K is an essential in R as a right R-subgroup of R .

- Every semiprime l. n. r. contains a maximal SRB* ideal .

- Direct sums and girect products of a family of l. n. r. are SRB(SRB*) if and only if each l. n. r. of the family is SRB(SRB*) .

- A direct summand ideal of a SRB l. n. r. is again a SRB l. n. r. .

- The right socie of a SRB l. n. r. is a direct sum of minimal ideals .