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Τι (ποιος) είναι quotient-ring - ορισμός

CONSTRUCTION IN ABSTRACT ALGEBRA

Factor ring; Residue class ring; Residue ring; Quotient Ring; Factor Ring; Quotient associative algebra

Quotient ring

In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal algebra.

https://en.wikipedia.org/wiki/Quotient_ring

Quotient space (linear algebra)

VECTOR SPACE CONSISTING OF AFFINE SUBSETS

Linear quotient space; Quotient vector space

In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by "collapsing" N to zero. The space obtained is called a quotient space and is denoted V/N (read "V mod N" or "V by N").

https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)

Total ring of fractions

Ring of fractions; Total fraction ring; Total ring of quotients; Total quotient ring

In abstract algebra, the total quotient ring, or total ring of fractions, is a construction that generalizes the notion of the field of fractions of an integral domain to commutative rings R that may have zero divisors. The construction embeds R in a larger ring, giving every non-zero-divisor of R an inverse in the larger ring.

https://en.wikipedia.org/wiki/Total_ring_of_fractions

Βικιπαίδεια

Quotient ring

In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal algebra. Starting with a ring R and a two-sided ideal I in R, a new ring, the quotient ring R / I, is constructed, whose elements are the cosets of I in R subject to special + and ⋅ operations. (Only the fraction slash "/" is used in quotient ring notation, not a horizontal fraction bar.)

Quotient rings are distinct from the so-called "quotient field", or field of fractions, of an integral domain as well as from the more general "rings of quotients" obtained by localization.

https://en.wikipedia.org/wiki/Quotient ring