منابع مشابه
Homomorphic Images of Polynomial Near-rings
A polynomial near-ring can mean one of several things. Here a polynomial near-ring is a near-ring of polynomials with the coefficients from a near-ring in the sense of van der Walt and Bagley. We describe quotients of such polynomial near-rings by principal ideals leading to generalizations of some well-known ring constructions. MSC 2000: 16Y30
متن کاملHomomorphic Images of an Infinite Product of Zero-dimensional Rings
Let R = Q a2A R a be an innnite product of zero-dimensional chained rings. It is known that R is either zero-dimensional or innnite-dimensional. We prove that a nite-dimensional homomorphic image of R is of dimension at most one. If each R a is a PIR and if R is innnite-dimensional, then R admits one-dimensional homomorphic images. However, without the PIR hypothesis on the rings R a , we prese...
متن کاملOn Rings Whose Associated Lie Rings Are Nilpotent
We call (i?) 1 the Lie ring associated with R, and denote it by 9Î. The question of how far the properties of SR determine those of R is of considerable interest, and has been studied extensively for the case when R is an algebra, but little is known of the situation in general. In an earlier paper the author investigated the effect of the nilpotency of 9î upon the structure of R if R contains ...
متن کاملIdeals Whose Associated Graded Rings Are Isomorphic to the Base Rings
Let k be a field. We determine the ideals I in a finitely generated graded k-algebra A, whose associated graded rings ⊕ n≥0 I/I are isomorphic to A. Also we compute the graded local cohomologies of the Rees rings A[It] and give the condition for A[It] to be generalized Cohen-Macaulay under the condition that A is generalized Cohen-Macaulay. MSC: 13A30, 13D45 Introduction Let k be a field and S ...
متن کاملGray Images of Constacyclic Codes over some Polynomial Residue Rings
Let be the quotient ring where is the finite field of size and is a positive integer. A Gray map of length over is a special map from to ( . The Gray map is said to be a ( )-Gray map if the image of any -constacyclic code over is a -constacyclic code over the field . In this paper we investigate the existence of ( )-Gray maps over . In this direction, we find an equivalent ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1970
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1970.35.727