The Faith-Menal conjecture says that every strongly right Johns ring is QF . The conjecture is also equivalent to say every right noetherian left FP -injective ring is QF . In this short article, we show that the conjecture is true under the condition( a proper generalization of left CS condition) that every nonzero complement left ideal is not small( a left ideal I is called small if for every...

Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of Ep, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field Q(πp) generated by the Frobenius element πp. When the curve has complex multiplication (CM), this is always a fixed field as the prime varies. However, when the curve has no CM, very little is known, not...

In this paper we show that finite rings for which the code equivalence theorem of MacWilliams is valid for Hamming weight must necessarily be Frobenius. This result makes use of a strategy of Dinh and López-Permouth.

Various forms of the extension problem are discussed for linear codes de ned over nite rings. The extension theorem for symmetrized weight compositions over nite Frobenius rings is proved. As a consequence, an extension theorem for weight functions over certain nite commutative rings is also proved. The proofs make use of the linear independence of characters as well as the linear independence ...

This paper studies Frobenius maps on injective hulls of residue fields of complete local rings with a view toward providing constructive descriptions of objects originating from the theory of tight closure. Specifically, the paper describes algorithms for computing parameter test ideals, and tight closure of certain submodules of the injective hull of residue fields of a class of well-behaved r...

The main purpose is to characterise continuous maps that are n-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius n-homomorphisms between two function spaces that correspond to n-branched coverings are determined completely. Several equivalent definitions of a Frobenius n-homomorphism are compared and some of their properties are proved. A...

This paper presents the classication of invariant subgroups automorphism groups regular elements obtained from nite local near-rings, appropriate algebraic structure to study non-linear functions on finite groups. Just as rings matrices operate vector spaces, near-rings In this paper, we construct classes zero symmetric near-ring characteristic pk; k = 1; 2 ; \(\ge\) 3 admitting frobenius deriv...