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3 Bulletin of the Polish Academy of Sciences. Mathematics

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Relations between Elements rpl - r and p⋅1 for a Prime p

Prószyński A.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

Vol. 62, no. 3

233--242

For any positive power n of a prime p we find a complete set of generating relations between the elements [r]=rn − r and p⋅1 of a unitary commutative ring.

On n-derivations and Relations between Elements rn−r for Some n

Maciejewski M., Prószyński A.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

Vol. 62, no 1

29--42

We find complete sets of generating relations between the elements [r]=rn−r for n=2l and for n=3. One of these relations is the n-derivation property [rs]=rn[s]+s[r], r,s∈R.

Relations between elements r²-r

Prószyński A.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 4

317-323

We prove that generating relations between the elements [r] = r² - r of a commutative ring are the following: [r + s] = [r] + [s] + rs[2] and [rs] = r²[s] + s[r].