FtsZFtsZ is a protein encoded by the ftsZ gene that assembles into a ring at the future site of bacterial cell division (also called the Z ring). FtsZ is a prokaryotic homologue of the eukaryotic protein tubulin. The initials FtsZ mean "Filamenting temperature-sensitive mutant Z." The hypothesis was that cell division mutants of E. coli would grow as filaments due to the inability of the daughter cells to separate from one another. FtsZ is found in almost all bacteria, many archaea, all chloroplasts and some mitochondria, where it is essential for cell division.
Zero ringIn ring theory, a branch of mathematics, the zero ring or trivial ring is the unique ring (up to isomorphism) consisting of one element. (Less commonly, the term "zero ring" is used to refer to any rng of square zero, i.e., a rng in which xy = 0 for all x and y. This article refers to the one-element ring.) In the , the zero ring is the terminal object, whereas the ring of integers Z is the initial object. The zero ring, denoted {0} or simply 0, consists of the one-element set {0} with the operations + and · defined such that 0 + 0 = 0 and 0 · 0 = 0.
MicrotubuleMicrotubules are polymers of tubulin that form part of the cytoskeleton and provide structure and shape to eukaryotic cells. Microtubules can be as long as 50 micrometres, as wide as 23 to 27 nm and have an inner diameter between 11 and 15 nm. They are formed by the polymerization of a dimer of two globular proteins, alpha and beta tubulin into protofilaments that can then associate laterally to form a hollow tube, the microtubule. The most common form of a microtubule consists of 13 protofilaments in the tubular arrangement.
Ring (mathematics)In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series.
Quotient ringIn 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.
CytoskeletonThe cytoskeleton is a complex, dynamic network of interlinking protein filaments present in the cytoplasm of all cells, including those of bacteria and archaea. In eukaryotes, it extends from the cell nucleus to the cell membrane and is composed of similar proteins in the various organisms. It is composed of three main components, microfilaments, intermediate filaments and microtubules, and these are all capable of rapid growth or disassembly dependent on the cell's requirements.
Ring homomorphismIn ring theory, a branch of abstract algebra, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is a function f : R → S such that f is: addition preserving: for all a and b in R, multiplication preserving: for all a and b in R, and unit (multiplicative identity) preserving: Additive inverses and the additive identity are part of the structure too, but it is not necessary to require explicitly that they too are respected, because these conditions are consequences of the three conditions above.
Local ringIn mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic number fields examined at a particular place, or prime. Local algebra is the branch of commutative algebra that studies commutative local rings and their modules. In practice, a commutative local ring often arises as the result of the localization of a ring at a prime ideal.
ActinActin is a family of globular multi-functional proteins that form microfilaments in the cytoskeleton, and the thin filaments in muscle fibrils. It is found in essentially all eukaryotic cells, where it may be present at a concentration of over 100 μM; its mass is roughly 42 kDa, with a diameter of 4 to 7 nm. An actin protein is the monomeric subunit of two types of filaments in cells: microfilaments, one of the three major components of the cytoskeleton, and thin filaments, part of the contractile apparatus in muscle cells.
Topological ringIn mathematics, a topological ring is a ring that is also a topological space such that both the addition and the multiplication are continuous as maps: where carries the product topology. That means is an additive topological group and a multiplicative topological semigroup. Topological rings are fundamentally related to topological fields and arise naturally while studying them, since for example completion of a topological field may be a topological ring which is not a field.
