20.500.12556/RUL-149823 Radikal kolobarja delo diplomskega seminarja Radical of a Ring V delu je predstavljen Jacobsonov radikal kolobarja skupaj s povezano teorijo in nekaterimi lastnosti. Z uvedbo kvazi-obrnljivosti je dokazana simetričnost definicije Jacobsonovega radikala. Opazujemo lastnosti na levo artinskih kolobarjih ter dokažemo Wedderburn-Artinov izrek, ki podaja klasifikacijo levo artinskih kolobarjev s trivialnim Jacobsonovim radikalom. Dokažemo tudi Jacobsonov izrek o gostoti ter podamo aplikacijo teorije Jacobsonovega radikala. The Jacobson radical of a ring is presented along with the related theory and certain properties. Quasi-invertibility is introduced with the focus of proving the symmetric property of the definition of the Jacobson radical. The Jacobson radical is further discussed in the context of Artinian rings and the Wedderburn-Artin Theorem is proven, providing a classification of left Artinian rings with a trivial Jacobson radical. The Jacobson Density Theorem is proven and an application of the Jacobson radical theory is demonstrated. Jacobsonov radikal artinski kolobarji Wedderburn-Artinov izrek Jacobsonov izrek o gostoti The Jacobson radical Artinian rings Wedderburn-Artin Theorem Jacobson Density Theorem true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2023-09-10 08:15:02 2023-09-10 08:15:03 2024-05-29 10:39:04 0000-00-00 00:00:00 2023 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 135614 163966723 9563.pdf 9563.pdf 1 6C9FDD58A8963978E79C438059F8B9F8 7a7b0bba04f92c813575fc3dff1bd355152d12afa11c500226e56e60656d3eef 61792438-4fa1-11ee-a2ce-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=174327 Fakulteta za matematiko in fiziko 0 0 0