<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "BEBERAPA SIFAT DERIVASI RING PRIMA"^^ . "The concept of derivation in ring theory originates from mathematicians’ desire\r\nto abstract and generalize the idea of differentiation in calculus into the realm\r\nof algebra. Gottfried Wilhelm Leibniz introduced the concept of derivation and\r\nthe symbol d to denote the process of differentiation, known as ”Leibniz notation”,\r\nalong with a rule of differentiation in calculus referred to as the ”Leibniz rule”. In\r\ncalculus, derivation is defined on the field of real numbers, which is a particular\r\nkind of ring known as a field. Every field is a prime ring, but the converse does\r\nnot necessarily hold. The abstraction and generalization of derivation into algebraic\r\nstructures are defined on rings in general, more specifically on prime rings.\r\nA ring derivation is a mapping from the ring to itself that satisfies the Leibniz rule.\r\nThe primeness and characteristic of a ring are key prerequisites in this study. This\r\nresearch focuses on the First and Second Posner’s Theorems. The First Posner’s\r\nTheorem states that in any prime ring of characteristic not equal 2, equipped with\r\ntwo derivations such that the composition of the two derivations is also a derivation,\r\nit follows that one of the derivations must be zero. The Second Posner’s Theorem\r\nasserts that in any prime ring of characteristic not equal 2, equipped with a nonzero\r\nderivation, if for every element a in the ring, the expression ad(a)−(a)a lies in the\r\ncenter of the ring, then the ring is commutative. Several counterexamples are provided\r\nto reinforce the necessity of the prime ring condition and the requirement that\r\nthe characteristic not be 2, as stipulated in both Posner’s Theorems. To support the\r\nFirst Posner’s Theorem, examples are given involving a prime ring and a non-prime\r\nring of characteristic 2. To support the Second Posner’s Theorem, an example is\r\nprovided of a non-prime, noncommutative ring with characteristic not equal to 2"^^ . "2025-06-10" . . . . "UIN SUNAN KALIJAGA YOGYAKARTA"^^ . . . "FAKULTAS SAINS DAN TEKNOLOGI, UIN SUNAN KALIJAGA YOGYAKARTA"^^ . . . . . . . . . "NIM.: 21106010030"^^ . "Diah Ajeng Nova Ananda"^^ . "NIM.: 21106010030 Diah Ajeng Nova Ananda"^^ . . . . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Text)"^^ . . . . . "21106010030_BAB-I_IV-atau-V_DAFTAR-PUSTAKA.pdf"^^ . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Text)"^^ . . . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Other)"^^ . . . . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Other)"^^ . . . . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Other)"^^ . . . . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Other)"^^ . . . . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Other)"^^ . . . . . . "preview.jpg"^^ . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Other)"^^ . . . . . . "medium.jpg"^^ . . . "BEBERAPA SIFAT DERIVASI RING PRIMA (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #71763 \n\nBEBERAPA SIFAT DERIVASI RING PRIMA\n\n" . "text/html" . . . "510 Mathematics (Matematika)" . .