Pronunciation: [mˈuːfaŋ] (IPA) 
The spelling of the word "moufang" can be confusing to those unfamiliar with its pronunciation. The correct IPA phonetic transcription of this word is /muːfæŋ/. The "mou" sounds like "moo" as in the sound a cow makes, while the "f" and "ng" sounds are pronounced as they appear. The "a" in the middle of the word is pronounced like the "a" in "cat". This unique combination of sounds creates the spelling for "moufang".
"Moufang" refers to a mathematical term that commonly denotes a type of algebraic structure known as Moufang algebra or Moufang loop. This term is named after the German mathematician Ruth Moufang, who significantly contributed to the development of these algebraic structures.
A Moufang algebra, or Moufang loop, is a set equipped with various operations that satisfy specific axioms. More precisely, it is a set together with an associative binary operation, often denoted as multiplication or composition, and an identity element. Additionally, a Moufang algebra possesses other properties, such as division algebras, which allow for the cancellation rule – if the product of two elements equals the product of two other elements, then these elements can be canceled out. Furthermore, the operation of left and right division is defined in a Moufang algebra.
Moufang algebras find applications in various branches of mathematics, including group theory, ring theory, and geometry. These structures have proven to be particularly useful in studying quasigroups, which are algebraic systems with only one operation that is not necessarily associative. Moufang algebras have provided insights into the properties of quasigroups, allowing mathematicians to better understand and analyze these structures.
In summary, "moufang" refers to a mathematical term that denotes a type of algebraic structure known as a Moufang algebra or Moufang loop, named after the mathematician Ruth Moufang.
The term "Moufang" has its etymology rooted in the name of a German mathematician, Ruth Moufang.
Ruth Moufang (1905-1977) was a prominent German mathematician who made significant contributions to the fields of abstract algebra and projective and non-associative geometry. She was particularly known for her work in non-associative algebras, which led to the development of structures known as "Moufang loops" or "Moufang sets".
These Moufang loops were named in honor of Ruth Moufang, and over time, the term "Moufang" became associated with these specific types of algebraic structures. Today, the term "Moufang" is commonly used to refer to the properties and structures related to Moufang loops or Moufang sets.
