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Algebras with finitely many orbits

✍ Scribed by Jan Okniński; Lex E. Renner

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
180 KB
Volume
264
Category
Article
ISSN
0021-8693

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✦ Synopsis

Any algebra of finite representation type has a finite number of two-sided ideals. But there are stronger finiteness conditions that should be considered here. We consider finite-dimensional Kalgebras that have only a finite number of left (respectively, principal left) ideals, up to conjugacy. We then characterize K-algebras A whose Jacobson radical satisfies J (A) 2 = 0, and with finitely many classes of principal left ideals. Finally, we consider basic algebras with J (A) 2 = 0. Here we characterize such algebras with finitely many classes of left ideals.

📜 SIMILAR VOLUMES

Some Boolean algebras with finitely many
Some Boolean algebras with finitely many distinguished ideals II
✍ Regina Aragón 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 291 KB

## Abstract We describe the countably saturated models and prime models (up to isomorphism) of the theory Th~prin~ of Boolean algebras with a principal ideal, the theory Th~max~ of Boolean algebras with a maximal ideal, the theory Th~ac~ of atomic Boolean algebras with an ideal such that the suprem

Some Boolean Algebras with Finitely Many
Some Boolean Algebras with Finitely Many Distinguished Ideals I
✍ Regina Aragón 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 993 KB

## Abstract We consider the theory Th~prin~ of Boolean algebras with a principal ideal, the theory Th~max~ of Boolean algebras with a maximal ideal, the theory Th~ac~ of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Th~sa~ of atomless Boolean algebras