{"product_id":"advances-in-the-theory-of-varieties-of-semigroups-9783031164965","title":"Advances in the Theory of Varieties of Semigroups","description":"\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003eThis monograph explores the development of the theory of varieties of semigroups and two related algebras, involution semigroups, and monoids, providing new results with detailed proofs and establishing this subfield as a matter of timely interest. \u003c\/blockquote\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 287 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 09 April 2023\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Birkhauser Verlag AG\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003eThis monograph delves into the intricate development of the theory of varieties of semigroups and two closely related algebras: involution semigroups and monoids. Through a comprehensive exploration, readers will gain a deeper understanding of the distinctions between these three types of varieties, which may initially appear counterintuitive. Moreover, the book presents novel results with detailed proofs, addressing previously unsolved fundamental problems. By offering both a comprehensive overview and showcasing the author's significant contributions to the field, this book aims to establish this subfield as a matter of timely interest. \u003cbr\u003eThe study of semigroups has played a pivotal role in mathematics since its inception, and the theory of varieties of semigroups has emerged as a crucial branch of this field. Varieties of semigroups are mathematical structures that generalize the concept of groups and allow for the study of semigroup operations in a more abstract setting. Involution semigroups and monoids are two related algebras that play a significant role in the theory of varieties of semigroups. Involution semigroups are semigroups that possess an involution operation, which is an operation that reverses the elements of the semigroup. Monoids are algebraic structures that consist of a set and a binary operation that combines two elements of the set to form a third element. \u003cbr\u003eThe development of the theory of varieties of semigroups has been a rich and complex process, with many important contributions made by mathematicians throughout history. One of the key milestones in the theory was the discovery of the Stone representation theorem by Harold Stone in 1940. This theorem states that every variety of semigroups is isomorphic to a variety of groups. This result provided a fundamental framework for the study of varieties of semigroups and has had a profound impact on the field. \u003cbr\u003eInvolution semigroups and monoids have also played a significant role in the theory of varieties of semigroups. Involution semigroups are particularly interesting because they allow for the study of semigroups with non-commutative multiplication. Monoids, on the other hand, are important because they are the building blocks of many other algebraic structures, such as groups, rings, and fields. \u003cbr\u003eThe study of varieties of semigroups has many applications in various fields, including mathematics, computer science, and physics. For example, semigroups are used in the study of quantum mechanics to describe the evolution of quantum systems. They are also used in the study of graph theory to represent and analyze complex networks. In addition, semigroups are used in the study of coding theory to design efficient data compression algorithms. \u003cbr\u003eDespite the many advances in the theory of varieties of semigroups, there are still many open questions and challenges that remain to be addressed. One of the most pressing challenges is the study of non-commutative varieties of semigroups. Non-commutative varieties of semigroups are semigroups that do not have a commutative multiplication operation. These semigroups are important because they arise in many applications, such as quantum mechanics and cryptography. \u003cbr\u003eAnother challenge is the study of semigroups with non-trivial automorphisms. Semigroups with non-trivial automorphisms are semigroups that possess an automorphism that is not the identity. These semigroups are important because they arise in many applications, such as group theory and number theory. \u003cbr\u003eIn conclusion, this monograph provides a comprehensive exploration of the development of the theory of varieties of semigroups and two related algebras: involution semigroups and monoids. Through a detailed analysis, readers will gain a deeper understanding of the distinctions between these three types of varieties, which may initially appear counterintuitive. The book also presents novel results with detailed proofs, addressing previously unsolved fundamental problems. By offering both a comprehensive overview and showcasing the author's significant contributions to the field, this book aims to establish this subfield as a matter of timely interest. \u003cbr\u003eAdvancements in the Theory of Varieties of Semigroups will appeal to researchers in universal algebra and will be particularly valuable for specialists in semigroups.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 518g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 240 x 168 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783031164965\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2023\u003c\/p\u003e","brand":"Edmond W. H. Lee","offers":[{"title":"Paperback \/ softback","offer_id":44307588415738,"sku":"9783031164965","price":41.64,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/noImage_1_f2fcba7c-a5ca-4b47-aca1-480c1c04692f.jpg?v=1688110087","url":"https:\/\/shulphink.com\/products\/advances-in-the-theory-of-varieties-of-semigroups-9783031164965","provider":"Shulph Ink","version":"1.0","type":"link"}