Naslov
The theta-transfer technique: on Noetherian involution rings and symmetry of primitivity

Autori
Širola, Boris

Izvornik
Glasnik Matematički (Series III) (0017-095X) 40(60) (2005);

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
antihomomorphism; antiautomorphic ring; involution ring; theta-homomorphism; prime ideal; primitive ideal; symmetry of primitivity

Sažetak
Let theta:R-->S be a ring anti-isomorphism. We study theta-homomorphisms between left R-modules E and right S-modules M, that is, homomorphisms of the additive groups Theta:E-->M satisfying Theta(r.x)=Theta(x)theta(r) for r in R and x in E. We also study the class of Noetherian involution rings and the problem of symmetry of primitivity. In particular, suppose that for every semiprimitive Noetherian involution ring which has exactly two minimal prime ideals both of these satisfy (SP). Then every prime ideal of an arbitrary Noetherian ring satisfies (SP) ; we say that a prime ideal P of some ring satisfies (SP), the symmetry of primitivity, if it holds that P is left primitive if and only if it is right primitive. Besides, as an interesting fact, we note that any factor ring of the enveloping algebra of the Lie algebra sl(2) over a field of characteristic zero is an involution algebra, and so it satisfies the Krull symmetry.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA