The properties are as follow:
The noun 'algebra' is an abstract noun, a word for a type of mathematics, the science that is concerned with numbers and their properties, relations, and operations; a word for a concept.
Edward M'William Patterson has written: 'Elementary abstract algebra' -- subject(s): Algebra 'Elementary abstract algebra [by] E.M. Patterson [and] D.E. Rutherford' -- subject(s): Abstract Algebra, Algebra, Abstract
The properties of a subgroup would include the identity of the subgroup being the identity of the group and the inverse of an element of the subgroup would be the same in the group. The intersection of two subgroups would be a separate group in the system.
yes
John A. Beachy has written: 'Abstract algebra' -- subject(s): Abstract Algebra, Algebra, Abstract 'Introductory lectures on rings and modules' -- subject(s): Modules (Algebra), Noncommutative rings
Gertrude Ehrlich has written: 'Fundamental concepts of abstract algebra' -- subject(s): MATHEMATICS / Algebra / Abstract, Abstract Algebra 'Fundamental concepts of abstract algebra' -- subject(s): Abstract Algebra 'Fundamental concepts of abstract algebra' -- subject(s): MATHEMATICS / Algebra / Abstract, Abstract Algebra
Dennis Kletzing has written: 'Abstract algebra' -- subject(s): Abstract Algebra
George Mackiw has written: 'Applications of abstract algebra' -- subject(s): Abstract Algebra
Abstract algebra is a field of mathematics that studies groups, fields and rings, which all belong to algebraic structures. Algebraic structure and abstract algebra are actually close to each other due to their similarity in topics.
When focusing upon abstract algebra, there are many different areas included within this topic such as groups, rings, modules and vector space. These all are part of the sequence to constructing abstract algebra.
Gary D. Crown has written: 'Abstract algebra' -- subject(s): Abstract Algebra
John W. Keesee has written: 'Elementary abstract algebra' -- subject(s): Abstract Algebra