Prilog teoriji poluprstena

Abstract

<p>Poluprsten je algebarska struktura (5, + , &bull;) sa dve binarne operacije u kojoj su&nbsp; (S,+ ) i (5, &bull;) polugrupe i druga je distributivna prema prvoj sa obe strane. U radu su uvedeni pojmovi p-polugrupe kao i p-poluprstena. Kažemo daje polugrupa ( S, + ) p-polugrupa ako (Vz G&nbsp; S)(3yG&nbsp; S)(x+py+x =&nbsp; y,py + x+py = z ). Poluprsten ( S, +.&bull;)zovemo p-poluprsten ako (Vz G&nbsp; S)(3yG&nbsp; S)(x + py + x = y,py + x + py = z,4p z2 = 4pz). Dokazano je da je svaka p-polugrupa pokrivena grupama koje su u potpunosti opisane. Takođe je pokazano da su p-poluprsteni pokriveni pretprsteni-ma. Za p = 4A; + 3&nbsp; (kG&nbsp; N0)ili p paran broj p-polugrupe, odnosno p-poluprsteni su varijeteti.</p>

<p>A semiring (5 ,+ ,-) is an algebric structure with two binary operations in which ( S, + ) and&nbsp; (S,&bull;) are semigroups, and the second operation is two-side dis&shy; tributive with respect to the first one. In the present paper notions of p-semigroup and p-semiring are introduced. We say that a semigroup (S&#39;, + ) is a p-semigroup if (Vx &pound; S)(3y &pound;&nbsp; S)(x + py + x = y,py + x + py = x).A semiring (S&#39;, + , &bull;) is called a p-semiring if (Vx &pound;&nbsp; S)(3y&pound;&nbsp; S)(x +py + x = y,py + x + py = x,4px2 = 4px). It is proved that each p-semigroup is covered by groups which are completely described. It is also proved that p-semirings are covered by prering. For&nbsp; p = 4k + 3 (k &pound; No) or for even p, the class of p-semigroups, respectively of p-semirings are varieties.</p>