Abstract. Let f : A → B and g : A → C be two commutative ring homomorphisms and let J and J ′ be two ideals of B and C, respectively, such thatThis paper investigates ring-theoretic properties of bi-amalgamations and capitalizes on previous works carried on various settings of pullbacks and amalgamations.In the second and third sections, we provide examples of bi-amalgamations and show how these constructions arise as pullbacks. The fourth section investigates the transfer of some basic ring theoretic properties to bi-amalgamations and the fifth section is devoted to the prime ideal structure of these constructions. All new results agree with recent studies in the literature on D'Anna-Finocchiaro-Fontana's amalgamations and duplications.

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Let f : A → B and g : A → C be two ring homomorphisms and let J and J be two ideals of B and C, respectively, such that f −1 (J) = g −1 (J ). The bi-amalgamation of A with (B, C) along (J, J ) with respect to (f, g) is the subring of B × C given byThe aim of this paper is to characterize the global dimension of bi-amalgamated algebras over pure ideals.

<p>The genetic algorithm (GA) is an adaptive metaheuristic search method based on the process of evolution and natural selection theory. It is an efficient algorithm used for solving the combinatorial optimization problems, e.g., travel salesman problem (TSP), linear ordering problem (LOP), and job-shop scheduling problem (JSP). The simple GA applied takes a long time to reach the optimal solution, the configuration of the GA parameters is vital for a successful GA search and convergence to optimal solutions, it includes population size, crossover operator, and mutation operator rates. Also, very recently, many research papers involved the GA in coding theory, In particular, in the decoding linear block codes case, which has heavily contributed to reducing the complexity, and guaranting the convergence of searching in fewer iterations. In this paper, an efficient method based on the genetic algorithm is proposed, and it is used for computing the Automorphisms groups of low density parity check (LDPC) codes, the results of the aforementioned method show a significant efficiency in finding an important set of Automorphisms set of LDPC codes.</p>

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