On Jónsson algebras over a commutative ring
نویسندگان
چکیده
منابع مشابه
Jónsson and HS Modules over Commutative Rings
Let R be a commutative ring with identity and let M be an infinite unitary R-module. (Unless indicated otherwise, all rings are commutative with identity 1 ̸ = 0 and all modules are unitary.)ThenM is called a Jónsson module provided every proper submodule of M has smaller cardinality than M. Dually, M is said to be homomorphically smaller (HS for short) if |M/N| < |M| for every nonzero submodule...
متن کاملOn Kalman models over a commutative ring
There is a good notion of rational functions with coefficients in a commutative ring. Using this notion, we easily obtain a neat generalization of Chapter 10 of the classical book by Kalman et al. to linear systems over an arbitrary commutative ring. The generalizations certainly exist already. However, we believe that the approach we present is more natural and straightforward. In this note we...
متن کاملUniformly Secondary Modules over Commutative Ring
In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.
متن کاملOn Fliess models over a commutative ring
Fliess models come as natural generalizations of classical polynomial models (D,N). As known, they are defined in terms of finitely generated modules and provide an adequate description of arbitrary linear systems (not necessarily observable or controllable). In this note we extend Fliess’ approach to linear systems defined over an arbitrary commutative ring. We believe that the exposition will...
متن کاملOn Rosenbrock models over a commutative ring
Rosenbrock’s notion of system equivalence is general in nature; it is a kind of equivalence which in algebra is often termed as stable. We have shown recently that Fuhrmann’s notion of system equivalence can be viewed as a homotopy equivalence, and as such is also general in nature. This note deals with a generalization of the theory of system equivalences from the field case to the commutative...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1987
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(87)80009-9