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Title: | Prilog teoriji poluprstena | Authors: | Budimirović Vjekoslav | Keywords: | semiring, semigroup, group, p-semigroup, p-semiring, prering, ring, isomorphism of semiring, variety;poluprsten, polugrupa, grupa, p-polugrupa, p-poluprsten, pretprsten, prsten, izomorfizam poluprstena, varijetet | Issue Date: | 17-Jul-2001 | Publisher: | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu University of Novi Sad, Faculty of Sciences at Novi Sad |
Abstract: | <p>Poluprsten je algebarska struktura (5, + , •) sa dve binarne operacije u kojoj su (S,+ ) i (5, •) 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 S)(3yG S)(x+py+x = y,py + x+py = z ). Poluprsten ( S, +.•)zovemo p-poluprsten ako (Vz G S)(3yG 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 (kG 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 (S,•) are semigroups, and the second operation is two-side dis­ 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', + ) is a p-semigroup if (Vx £ S)(3y £ S)(x + py + x = y,py + x + py = x).A semiring (S', + , •) is called a p-semiring if (Vx £ S)(3y£ 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 p = 4k + 3 (k £ No) or for even p, the class of p-semigroups, respectively of p-semirings are varieties.</p> |
URI: | https://open.uns.ac.rs/handle/123456789/27403 |
Appears in Collections: | PMF Teze/Theses |
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