A simple but elegant result of Rival states that every sublattice _{L}

**Key Words:**

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Functionfinite distributive lattice, representation, embedding, product of chains.

We introduce the Leavitt path algebras of ultragraphs and we characterize their ideal structures. We then use this notion to introduce and study the algebraic analogy of Exel-Laca algebras.

**Key Words:**

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Functionultragraph *C*^{∗}-algebra, Leavitt path algebra, Exel-Laca algebra.

A module

**Key Words:**

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Functionfully invariant submodule, FI-extending, GFI-extending.

Let (

**Key Words:**

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Functioncommutative ring, ring extension, minimal ring extension, inert extension, maximal ideal, minimal ﬁeld extension, quasi-local ring, integrality, pullback.

A ring

**Key Words:**

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Functionquasi-reversible ring, matrix ring.

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated appl...

**Key Words:**

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Functionfractional calculus, fractional-order integrals, fractional-order derivatives, diﬀerential equations, Integral equations, Cauchy-Goursat integral formula, diﬀerintegral equations, special functions, mathematical physics, Fuchsian and

In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of...

**Key Words:**

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric FunctionBanach function algebra, diﬀerentiable Lipschitz algebras, extended Lipschitz algebra, maximal ideal space, rational functions. This work was supported by Urmia University.