منابع مشابه
On the Ideals and Automorphisms of Non-associative Rings
Introduction. Relations between the multiplication ring of a ring (= non-associative ring)1 and the ring itself have been pointed out by a number of writers [l-7]. In the present note it is shown that the ideal lattice of a ring with unit element is isomorphic to the sublattice of all right ideals of the multiplication ring which contain the annihilator of the unit. A corresponding result is ob...
متن کاملOn groups of similitudes in associative rings
Let R be an associative ring with 1 and R the multiplicative group of invertible elements of R. In the paper, subgroups of R which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the cor...
متن کاملHomotopy Theory of Associative Rings
A kind of unstable homotopy theory on the category of associative rings (without unit) is developed. There are the notions of fibrations, homotopy (in the sense of Karoubi), path spaces, Puppe sequences, etc. One introduces the notion of a quasi-isomorphism (or weak equivalence) for rings and shows that similar to spaces the derived category obtained by inverting the quasiisomorphisms is natura...
متن کاملFoxby Equivalence over Associative Rings
We extend the definition of a semidualizing module to associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule C. We then study the classes of C-flats, C-projectives, and C-injectives, and use them to provide a characterization of the modules in the Auslander and Bass classes. We extend Foxby equivalence to this new setting. This...
متن کاملOn One-sided Lie Nilpotent Ideals of Associative Rings
We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of R. One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form [. . . [[r1, r2], . . .], rn−1...
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ژورنال
عنوان ژورنال: Mathematics and Statistics
سال: 2021
ISSN: 2332-2071,2332-2144
DOI: 10.13189/ms.2021.090212