Some Algebraic Properties of Polynomial Rings

Gray 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 ...

Algorithmic Properties of Polynomial Rings

In this paper we investigate how algorithms for computing heights, radicals, unmixed and primary decompositions of ideals can be lifted from a Noetherian commutative ring R to polynomial rings over R. It is a standard problem in mathematics to study which properties of a mathematical structure are preserved in derived structures. A typical result of this kind is the Hilbert Basis Theorem which ...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Differential Polynomial Rings of Triangular Matrix Rings

extensions of some polynomial inequalities to the polar derivative

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