Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.

In this paper, we study skew cyclic codes with arbitrary length over the ring $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$ where $p$ is an odd prime and $% u^{2}=0$. We characterize all skew cyclic codes of length $n$ as left $% R[x;\theta ]$-submodules of $R_{n}=R[x;\theta ]/\langle x^{n}-1\rangle $. We find all generator polynomials for these codes and describe their minimal spanning sets. Moreover, an...

We introduce the notion of E-depth graded modules over polynomial rings to measure depth certain Ext modules. First, we characterize with (sufficiently) large as those whose partial general initial submodules preserve Hilbert function local cohomology supported at irrelevant maximal ideal, extending a result Herzog and Sbarra on sequentially Cohen-Macaulay Second, describe cone tables sufficien...

arising from . We introduce the notion of p-exactness for a sequence and show that any interval of (*) not including Mn 2 or Mn+1 2 respectively, is p-exact for any prime p>0. This result can be extended to various submodules and quotient modules, and we give general constructions for permutation groups on 0 of order not divisible by p. If an interval of (*) , or an equivalent sequence arising ...

Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum....

In this paper, a novel architecture for a finite field integer multiplier based on a superset of the triple moduli set {2-1,2,2+1} is presented. The superset is constructed by adding extra moduli of the form 2±1 (for any non-zero integer n) to extend its range. The multiplier uses index transform approach whereby multiplication is carried out by index addition, and is organized into submodules ...

For a module M over commutative ring R with identity, let RSpec(M) denote the collection of all submodules L Msuch that ?(L:M) is prime ideal and equal to (rad L:M). In this article, we topologies topology which enjoys analogs many properties Zariski on spectrum Spec(M) (as subspace topology). We investigate topological space from point view spectral spaces by establishing interrelations betwee...

In this paper, we relate combinatorial conditions for polarizations of powers the graded maximal ideal with rank on submodules generated by collections Young tableaux. We apply discrete Morse theory to hypersimplex resolution introduced Batzies–Welker show that L-complex Buchsbaum and Eisenbud is supported a CW-complex. then translate “spanning tree condition” Almousa–Fløystad–Lohne characteriz...